{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "375719f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff2426b0",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "## Overview\n",
    "    > For linear regression model, 4 different approches are listed below\n",
    "    1. by matrix formula\n",
    "    2. by Batch Gradient Descent\n",
    "    3. by Stochastic Gradient Descent\n",
    "    4. by Mini-batch Gradient Descent\n",
    "## Formula\n",
    "    > model formula\n",
    "$$\n",
    "    \\hat Y = \\theta^T \\cdot X\n",
    "$$\n",
    "    \n",
    "    > cost function - RMSE\n",
    "$$\n",
    "    MSE = \\frac{1}{m}\\sum_{i}^{m}{{(Y - \\theta^T \\cdot X)}^2}\n",
    "$$\n",
    "\n",
    "    > optimized result\n",
    "$$\n",
    "    \\theta = {(X^TX)}^{-1}X^TY\n",
    "$$\n",
    "\n",
    "    > sklearn.linear_model could reach this by calling LinearRegression class\n",
    "    > for sklearn, intercept_ is bias term, corresponding to all ones column\n",
    "    > the rest parameters are stored in coef_, its number depends on features number in X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e0e9bbbe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.95065095] [3.97343684]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# generate linear data with random noises\n",
    "X_raw = np.random.rand(100,1)\n",
    "X = np.sort(X_raw,axis=0)\n",
    "y = 3 + 4 * X + np.random.randn(100,1)\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X,y)\n",
    "intercept = lin_reg.intercept_\n",
    "slop = lin_reg.coef_\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,8),\n",
    "                     facecolor='whitesmoke',\n",
    "                     edgecolor='gray')\n",
    "scatter = ax.scatter(X, y, marker=\"x\", color='blue', label='raw')\n",
    "linear = ax.plot(X, intercept+slop*X, lw=1, color='red', label='predict')\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.grid(alpha=0.4)\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\")\n",
    "print(intercept, slop[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3521f91",
   "metadata": {},
   "source": [
    "## GD\n",
    "    > BGD and SGD work under the same concept, which is updating parameter vector with gradient of cost function with respect to parameter vector\n",
    "    > the difference lies in training data selection. BGD will take all data into calculation, which means that data matrix is of size (m*n), while SGD only takes one random data point for training, that is a single (1* n) vector, and for the purpose of preventing over-striding which would possibly leads to divergence, we introduce learning rate to fine-tune gradient for each sgd iteration. We always tends to gradually decreate learning rate with training progressing on. This process is also called simulated annealing.\n",
    "    > Mini-batch GD is of the same manner, which slightly increases number of data points in each iteration. Make sure to distingush term iteration and epoch.\n",
    "1. BGD is not supported in sklearn toolset, while we could find <font color=sapphire><b>SGDRegressor in sklearn.linear_model</b></font>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7841718d",
   "metadata": {},
   "source": [
    "    > formula for gradient\n",
    "$$\n",
    "        \\nabla_{\\theta}MSE(\\theta) = \\frac{2}{m}X^T\\cdot(X\\cdot\\theta - y)\n",
    "$$\n",
    "\n",
    "    > formulat for paramter vector update\n",
    "$$\n",
    "        \\theta^{(next \\space step)} = \\theta - \\eta \\cdot \\nabla_{\\theta} MSE(\\theta)\n",
    "$$\n",
    "\n",
    "    > simulated annealing formula\n",
    "$$\n",
    "    \\eta = \\frac{t_0}{f(epoch)+ t_1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b553832b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 0: \n",
      "[[3.48066902]\n",
      " [2.99980566]]\n",
      "============================\n",
      "epoch 40: \n",
      "[[3.03284885]\n",
      " [3.79988505]]\n",
      "============================\n",
      "epoch 80: \n",
      "[[3.03433775]\n",
      " [3.84889629]]\n",
      "============================\n",
      "epoch 120: \n",
      "[[2.98781888]\n",
      " [3.84842256]]\n",
      "============================\n",
      "epoch 160: \n",
      "[[3.03626446]\n",
      " [3.904919  ]]\n",
      "============================\n",
      "epoch 200: \n",
      "[[2.9725495 ]\n",
      " [3.89440025]]\n",
      "============================\n",
      "epoch 240: \n",
      "[[2.98414388]\n",
      " [3.91225125]]\n",
      "============================\n",
      "epoch 280: \n",
      "[[2.9684514 ]\n",
      " [3.89940945]]\n",
      "============================\n",
      "epoch 320: \n",
      "[[2.97917911]\n",
      " [3.90897026]]\n",
      "============================\n",
      "epoch 360: \n",
      "[[2.9776023 ]\n",
      " [3.91629579]]\n",
      "============================\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# total training epoch, hyperparameter\n",
    "n_epoch = 400\n",
    "# number of data points, or whole batch size\n",
    "m = 100\n",
    "# simulated annealing parameter, hyperparameter\n",
    "t0, t1 = 5, 50\n",
    "# initialization of parameter vedtor \\theta\n",
    "theta = np.random.randn(2,1)\n",
    "# adding all zero power term(interception) to training dataset\n",
    "X_b = np.c_[np.ones((100,1)),X.reshape(100,1)]\n",
    "# store MSE\n",
    "mse_list = []\n",
    "# store theta\n",
    "theta_list = []\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "for epoch in range(n_epoch):\n",
    "    for i in range(m):\n",
    "        theta_list.append(theta)\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index,:]\n",
    "        yi = y[random_index,:]\n",
    "        grad = 2*xi.reshape(2,1).dot(xi.reshape(1,2).dot(theta)-yi)\n",
    "        mse = pow(xi.reshape(1,2).dot(theta) - yi, 2)\n",
    "        mse_list.append(mse)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * grad\n",
    "    if epoch % 40 == 0:\n",
    "        print(\"epoch %s: \"% epoch)\n",
    "        print(theta)\n",
    "        print(\"============================\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a448fab8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.99128402],\n",
       "       [3.92453162]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "42d384bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(16,4))\n",
    "ax.plot(np.asarray(list(range(len(mse_list))))[::40], np.asarray(mse_list).flatten()[::40],label=\"mse_value\")\n",
    "ax.set_title(\"mse of SGD\")\n",
    "ax.legend(loc=\"upper right\")\n",
    "ax.grid(alpha=0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "158507ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(6,4))\n",
    "ax.scatter(X, y, marker=\".\", color=\"blue\", lw=0.5, label=\"raw\")\n",
    "iter_op = 1\n",
    "for index, (intercept, slope) in enumerate(theta_list):\n",
    "    if index == 0:\n",
    "        ax.plot(X, slope*X+intercept, lw=0.5,ls=\"--\",color=\"red\")\n",
    "    if index % iter_op == 0 and index != 0:\n",
    "        ax.plot(X, slope*X+intercept, lw=0.5,ls=\"-\",color=\"blue\")\n",
    "        iter_op *= 2\n",
    "ax.plot(X, theta[1]*X+theta[0], lw=1,ls=\"-\",color=\"magenta\", label=\"predict\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regressor fitting results\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\",rotation=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "505b8b11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(6,4))\n",
    "theta_pts = np.asarray(theta_list).flatten().reshape(len(theta_list),2)\n",
    "ax.plot(theta_pts[:,1],theta_pts[:,0], lw=0.5, color=\"blue\",label=\"SGD\")\n",
    "ax.scatter(theta_pts[:,1],theta_pts[:,0], marker='.', lw=0.1, color='blue')\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"SGD searching routine\")\n",
    "ax.set_xlabel(r'$\\theta_1$')\n",
    "ax.set_ylabel(r'$\\theta_0$', rotation=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c6b3216",
   "metadata": {},
   "source": [
    "# Polynomial Regression\n",
    "1. adding higher power terms by manipulating exsting data\n",
    "2. <font color=burgendy><b>sklearn.preprocessing PolynomialFeatures</b></font> could do, or simply numpy columnar manipulation would do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e7d99fe8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 30)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "%matplotlib inline\n",
    "\n",
    "# prepare input noise-added data\n",
    "m = 100\n",
    "X = np.sort(12*np.random.rand(m,1)-6, axis=0)\n",
    "y = 0.5 * X**3 + 2.7 * X**2 + 3 + 12 * np.random.randn(m,1)\n",
    "\n",
    "poly_features_3 = PolynomialFeatures(degree=3, include_bias=False)\n",
    "poly_features_30 = PolynomialFeatures(degree=30, include_bias=False)\n",
    "X_poly_3 = poly_features_3.fit_transform(X)\n",
    "X_poly_30 = poly_features_30.fit_transform(X)\n",
    "print(X_poly_30.shape)\n",
    "\n",
    "lin_reg_3 = LinearRegression()\n",
    "lin_reg_3.fit(X_poly_3,y)\n",
    "lin_reg_30 = LinearRegression()\n",
    "lin_reg_30.fit(X_poly_30,y)\n",
    "\n",
    "y_3 = lin_reg_3.intercept_ * np.ones_like(X) + X_poly_3.dot(lin_reg_3.coef_.T)\n",
    "y_30 = lin_reg_30.intercept_ * np.ones_like(X) + X_poly_30.dot(lin_reg_30.coef_.T)\n",
    "\n",
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(6,4))\n",
    "ax.scatter(X, y, marker='.', color=\"b\", lw=0.1)\n",
    "ax.plot(X, y_3, lw=0.5, ls=\"-\", color=\"red\", label=\"power-3 regression\")\n",
    "ax.plot(X, y_30, lw=0.5, ls=\"--\", color=\"green\", label=\"power-30 regression\")\n",
    "ax.legend(loc='upper left')\n",
    "ax.set_title(\"polynomial regression at different degrees\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\", rotation=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dad9db86",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.52237757] [[-0.56619705  2.62603652  0.52696497]]\n"
     ]
    }
   ],
   "source": [
    "print(lin_reg_3.intercept_, lin_reg_3.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb5ec0ea",
   "metadata": {},
   "source": [
    "# learning curve\n",
    "1. one efficient way to decide wether a model is over fitting or underfitting.\n",
    "2. main trick is increase volume of training set and testing set gradually and compare their cost function value, in regression case, this is MSE or RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f83acd98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's take cubic function above\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "    # list store mse of training and testing\n",
    "    train_errors, test_errors = [], []\n",
    "    # increase volume of training set gradually\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_pred = model.predict(X_train[:m])\n",
    "        y_test_pred = model.predict(X_test)\n",
    "        train_errors.append(mean_squared_error(y_train[:m],y_train_pred))\n",
    "        test_errors.append(mean_squared_error(y_test, y_test_pred))\n",
    "    plt.plot(np.sqrt(train_errors),lw=2,ls='-.', color='red', label=\" training set\")\n",
    "    plt.plot(np.sqrt(test_errors),lw=3,ls='-', color='blue', label=\" validation set\")\n",
    "    plt.legend(loc=\"upper right\")\n",
    "    plt.title(\"learning curve\")\n",
    "    plt.xlabel(\"Training set size\")\n",
    "    plt.ylabel(\"RMSE\", rotation=0)\n",
    "\n",
    "# this case we'll show underfitting\n",
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1029c7ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "polynomial_regression = Pipeline([\n",
    "    (\"poly_features\", PolynomialFeatures(degree=4, include_bias=False)),\n",
    "    (\"sgd_red\", LinearRegression())\n",
    "    ])\n",
    "plot_learning_curves(polynomial_regression, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eb46544",
   "metadata": {},
   "source": [
    "# Regularization\n",
    "1. basic concept is adding terms with regards to parameter vector on training cost function to constrain paramters\n",
    "2. usually cost function in training set is different from that in test set.\n",
    "3. lasso and elastic net tends to discard features that contribute less to label or target\n",
    "## Ridge Regression\n",
    "$$\n",
    "    J(\\theta) = MSE(\\theta) + \\alpha \\frac{1}{2}\\sum_{i=1}^{n}{{\\theta_{i}}^2}\n",
    "$$\n",
    "\n",
    "    > closed-form formula\n",
    "\n",
    "$$\n",
    "    \\hat \\theta = {(X^T \\cdot X + \\alpha I)}^{-1} + X^T \\cdot y\n",
    "$$\n",
    "* where $I$ is one $(n*n)$ identity matrix\n",
    "\n",
    "> linear_model Ridge or linear_model SGDRegressor(penalty='l2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8f4fd006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X_poly_30, y)\n",
    "y_pred_ridge = ridge_reg.predict(X_poly_30)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=0.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_pred_ridge, '-g', label=\"ridge regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdb5f3d4",
   "metadata": {},
   "source": [
    "## Lasso\n",
    "$$\n",
    "    J(\\theta) = MSE(\\theta) + \\alpha \\sum_{i=1}^{n}{|\\theta_{i}|}\n",
    "$$\n",
    "\n",
    "while this time subgradient formula is like:\n",
    "$$\n",
    "    g(\\theta,J) = \\nabla_{\\theta} MSE + \\alpha \\cdot sign(\\theta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f1e2d146",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "import warnings \n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "lasso_reg = Lasso(alpha=0.01)\n",
    "lasso_reg.fit(X_poly_30, y)\n",
    "y_pred_lasso = lasso_reg.predict(X_poly_30)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_pred_lasso, '-g', label=\"lasso regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f226f8e2",
   "metadata": {},
   "source": [
    "## Elastic Net\n",
    "$$\n",
    "    J(\\theta) = MSE + r\\alpha \\sum_{i=1}^{n}{|\\theta_i|} + \\frac{1-r}{2}\\alpha\\sum_{i=1}^{n}{{\\theta_i}^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "6b47d871",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "# l1_ratio here is equal to r in formula\n",
    "elastic_net = ElasticNet(alpha=0.1,l1_ratio=0.5)\n",
    "elastic_net.fit(X_poly_30, y)\n",
    "y_pred_elanet = elastic_net.predict(X_poly_30)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_pred_elanet, '-g', label=\"elastic net regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7db06c2c",
   "metadata": {},
   "source": [
    "## early stopping\n",
    "stop training when rmse(cost function) reaches its minimum, which means we might reach global minimum\n",
    "\n",
    "<font color=purple><b>SGDRegressor parameters overview</b></font>\n",
    "\n",
    "    > loss='squared_error',\n",
    "    > penalty='l2',\n",
    "    > alpha=0.0001,\n",
    "    > l1_ratio=0.15,\n",
    "    > fit_intercept=True,\n",
    "    > max_iter=1000,\n",
    "    > tol=0.001,\n",
    "    > shuffle=True,\n",
    "    > verbose=0,\n",
    "    > epsilon=0.1,\n",
    "    > random_state=None,\n",
    "    > learning_rate='invscaling',\n",
    "    > eta0=0.01,\n",
    "    > power_t=0.25,\n",
    "    > early_stopping=False,\n",
    "    > validation_fraction=0.1,\n",
    "    > n_iter_no_change=5,\n",
    "    > warm_start=False,\n",
    "    > average=False,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5982f003",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13039\n",
      "[35.14992894] [ -2.92631781  24.8691139   47.15111303  11.38240364   1.75001538\n",
      " -10.63858871 -11.60628243 -12.63445131  -7.53152717  -5.9873081\n",
      "   0.10995271   1.55624847   5.97995672   7.07524291   8.92784955\n",
      "   9.93820586   9.26545079  10.36389661   7.64523944   8.81862955\n",
      "   4.68291693   5.79026561   0.86445305   1.71171126  -3.45264913\n",
      "  -3.0586188   -8.01399706  -8.23526585 -12.64193773 -13.59703184]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.base import clone\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# for higher-power regression model, standardization is necessary\n",
    "std_scaler = StandardScaler()\n",
    "X_scaled_30 = std_scaler.fit_transform(X_poly_30)\n",
    "single_sgd_reg = SGDRegressor(max_iter=1, warm_start=True,  penalty=None,\n",
    "                              learning_rate=\"constant\", eta0=0.0005)\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "cnt = 0\n",
    "for epoch in range(20000):\n",
    "    single_sgd_reg.fit(X_scaled_30,y)\n",
    "    y_single_sgd_pred = single_sgd_reg.predict(X_scaled_30)\n",
    "    single_error = mean_squared_error(y_single_sgd_pred, y)\n",
    "    if single_error < minimum_val_error:\n",
    "        minimum_val_error = single_error\n",
    "        best_epoch = epoch\n",
    "        best_model = clone(single_sgd_reg)\n",
    "        cnt = 0\n",
    "    else:\n",
    "        cnt += 1\n",
    "    # if mse doesn't increase in 20 consecutive epoch, \n",
    "    # assert convergence and leave iteration\n",
    "    if cnt >= 20:       \n",
    "        break\n",
    "\n",
    "print(best_epoch)\n",
    "print(single_sgd_reg.intercept_, single_sgd_reg.coef_)\n",
    "\n",
    "best_model.fit(X_scaled_30, y)\n",
    "y_single_pred = best_model.predict(X_scaled_30)\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_single_pred, '-g', label=\"early stop strategy regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b77bf670",
   "metadata": {},
   "source": [
    "# Logistic Regression\n",
    "1. commonly used to estimate the probability that an instance belongs to a particular class, all outputs of model will be processed through one continuously differentiable function.\n",
    "$$\n",
    "    \\sigma(t) = \\frac{1}{1 + e^{-t}}\n",
    "$$\n",
    "2. output of model will be precessed by\n",
    "$$\n",
    "    \\hat p = h_{\\theta}(x) = \\sigma(\\theta^T \\cdot \\vec x)\n",
    "$$\n",
    "3. for a sigmoid function, the threshold is always set as 0.5, this is used in one binary classifier\n",
    "4. cost function of logistic regression\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "    J(\\theta) & = & \\frac{1}{m}L(\\theta) \\\\\n",
    "    L(\\theta) & = & \\sum_{i=1}^{m}{y_{i}logp(x_i)} + \\sum_{i=1}^{m}{(1-y_{i})log(1-p(x_i))} \\\\\n",
    "    p(x_i) & = & \\sigma(\\theta^{T}x_{i}) \\\\\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "5. derivitive form of cost function\n",
    "$$\n",
    "    \\frac{\\partial J(\\theta)}{\\partial \\theta_{j}} = \\frac{1}{m}[\\sigma(\\theta^{T}x) - y]x_j\n",
    "$$\n",
    "6. note that x here is a $(m,n)$ matrix where m stands for m features and n stands for n data points(entries)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cae9dc2d",
   "metadata": {},
   "source": [
    "## sigmoid function\n",
    "1. transfer $\\theta^T \\cdot x \\in R$ to $\\hat y \\in (0, 1)$ set\n",
    "2. also, sigmoid is a cdf function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f1714be2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA/IAAAGbCAYAAABnBquDAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAA9hAAAPYQGoP6dpAABp50lEQVR4nO3deVhU5f/G8XtYVRQUFMTEfUXNJdcs91KzcsndXHMpU8vCNZd+laZpLlmpmKaZmmZqZZq5oOW+ZH6tLPctQVRKEJR1fn+cGJ1ARUQOA+/Xdc0FHJ5z5jNzZg7cc57zPJbo6GirAAAAAACAQ3AyuwAAAAAAAJB2BHkAAAAAABwIQR4AAAAAAAdCkAcAAAAAwIEQ5AEAAAAAcCAEeQAAAAAAHAhBHgAAAAAAB0KQBwAAAADAgRDkAQAAAABwIAR5AAD+Y+XKlapZs6Z8fHzk4eGhQ4cOmVbL7t27NWHCBP3zzz8pfteiRQu1aNEi84tKgwkTJsjDw0OXL182uxQAALIdF7MLAAAgK7l06ZL69u2rJ554QtOnT5e7u7vKli1rWj27d+/WxIkT9fzzzyt//vx2v5s+fbo5RQEAAFMR5AEAuMXx48cVHx+vzp076/HHHze7nDuqWLGi2SUAAAAT0LUeAIB/9e/fX82aNZMk9ejRQx4eHrau67frxt6/f3+7QH3mzBl5eHhoxowZ+uCDDxQYGChfX181btxYe/fuTbH+vn371L59ewUEBMjb21uVK1fWsGHDJBnd09944w1JUmBgoDw8POTh4aEff/zxtjVFRETo1VdfVZkyZZQ/f35VqlRJb775pmJjY+3aeXh46LXXXtPSpUtVo0YNFSxYUHXq1NH69evv+jwlJSVp8uTJqlatmnx8fFSkSBHVrl1bH330UYq24eHh6tmzp/z9/VWiRAm9+OKLunr1ql2bGzduaNy4cQoMDFT+/PlVpkwZDR061O5ygtGjR8vf31+JiYm2Za+//ro8PDzseiZcuXJFefPm1ezZs+/6OAAAcFSckQcA4F8jR45UzZo1NXToUL355ptq2LCh8uXLl65tBQcHq1y5cnrvvfckSW+99ZbatWun3377TV5eXpKkjRs3qkOHDipfvrzeffddBQQE6MyZM9q8ebMkqVevXvr77781e/ZsLVu2TIULF5YkVahQIdX7vHHjhlq2bKlTp07pjTfeUOXKlbVz505NnTpV//vf/7Rq1Sq79t9//70OHDigMWPG2D586Ny5s3755ReVLFnyto9t2rRpmjBhgkaMGKH69esrPj5eR48eTRHQJalbt2567rnn1LNnT/32228aP368JGnOnDmSJKvVqk6dOmnr1q0KCgrSo48+ql9//VUTJkzQnj17FBISInd3dzVu3FgzZ87U/v37VadOHUlSSEiIcufOrS1btmjo0KGSpK1bt8pqtapx48Zp21EAADgggjwAAP8qVaqULSSXKVNGtWvXTve28ubNq6+++krOzs6SJH9/fzVo0EA//PCDOnToIEl67bXXFBAQoG3btilXrly2dXv06CFJeuihh1S0aFFJUtWqVVW8ePE73ueSJUv066+/avHixWrXrp0kqWnTpvLw8NDYsWO1efNmNW3a1Nb++vXrWrt2re3DimrVqqlMmTL66quvFBQUdNv72b17typVqmTrLSBJTzzxRKpte/ToYQvZTZo00cmTJ/XZZ59p9uzZslgs2rRpkzZt2qR33nnH1q5p06YqWrSoevTooaVLl6p3796qX7++3NzcFBISojp16ujChQv6888/9dprr2n27NmKjY2Vu7u7QkJC5O/vf9sPOwAAyA7oWg8AwAPQokULW4iXpMqVK0uSzp49K0k6duyYTp48qR49etiF+Puxbds2eXh4qG3btnbLn3/+eUnG2epbNWjQwK7HgZ+fnwoVKqRz587d8X5q1qypw4cP69VXX9XGjRsVGRl527atWrWy+7ly5cq6ceOGwsPDbTXfWmOydu3aycPDw1Zznjx5VKdOHYWEhEiSNm/erPz58+vVV19VXFycdu7cKck4S8/ZeABAdkeQBwDgAfD29rb72d3dXZLR/V2SbVq2hx56KMPu88qVK/Lz85PFYrFb7uvrKxcXF0VERNgt9/HxSbENd3d3Xb9+/Y73ExQUpIkTJ2rv3r1q27atAgIC9NRTT+nnn39O0fa/z4Obm5ukm89DRESEXFxcVKhQIbt2FotFfn5+unLlim1Z8jgD0dHRCgkJUcOGDeXj46Pq1asrJCREp0+f1unTpwnyAIBsjyAPAEAauLu7pxgwTpJd0LwXBQsWlCT99ddf91XXrXx8fBQeHi6r1Wq3PDw8XAkJCakG9/RwcXHRkCFDtHPnTp0/f14LFy7UX3/9pdatWysmJuaetuXt7a2EhARdunTJbrnVatXFixftam7UqJHi4uK0fft2bd26VU2aNLEt37Jli7Zs2SJJBHkAQLZHkAcAIA2KFy+u48eP24X5K1euaM+ePenaXtmyZVWqVCktXrw41Q8IkiWfyb/bWXLJCLTXrl3Tt99+a7d86dKltt9ntPz586tt27bq37+/IiIidObMmXtaP7mmL774wm75mjVrFB0dbRfKa9asKU9PT3300Ue6ePGiLcg3btxYhw4d0ldffaWKFSvK39///h4UAABZHIPdAQCQBl26dNH8+fP1wgsvqFevXoqIiND06dPTPaq9ZIz+3qFDBzVq1EiDBg1SQECAzp07p02bNunTTz+VJFWqVEmS9PHHH6tbt25ydXVV2bJlU73frl27au7cuerfv7/OnDmjSpUqadeuXZoyZYqaN29uC773q3379goMDLRNW3f27Fl99NFHKlasmMqUKXNP22ratKmaNWumsWPHKioqSnXr1rWNWl+1alV16dLF1tbZ2VmPPfaY1q1bpxIlSqhUqVKSpHr16snd3V1bt27VSy+9lCGPEQCArIwz8gAApEG9evUUHBysI0eOqFOnTnrvvfcUFBSkxx9/PN3bfOKJJ/TDDz+ocOHCGjZsmNq0aaNJkybJ19fX1qZBgwYKCgrSunXr1KxZMz3++OM6ePBgqtvLlSuX1q9fr06dOmnGjBlq27atPv/8c73yyitatmxZuuv8rwYNGmjHjh165ZVX9Mwzz+itt95So0aNtGHDBrm6ut7TtiwWi5YvX67BgwfbRtufOXOmunTponXr1tl6JCRLPkN/65l6d3d31atXT5Iy7MMKAACyMkt0dLT17s0AAAAAAEBWwBl5AAAAAAAcCEEeAAAAAAAHQpAHAAAAAMCBEOQBAAAAAHAgBHkAAAAAABwIQR4AAAAAAAdCkAcAAAAAwIEQ5AEA2V7//v1VsWJFs8u4Kw8PD02YMOGu7RYvXiwPDw+dOXPmrm1nz56tKlWqKH/+/PLw8NA///yTAZWmz/fff3/bx1exYkX1798/kytKm/79+8vX19fsMgAAsHExuwAAAB60kSNHauDAgWaXcVchISF66KGHMmx7hw4dUlBQkHr16qVu3brJxcVF+fLly7Dt36sffvhBc+fO1RtvvJHid8uWLZOnp6cJVQEA4HgI8gCAbK9UqVJml5AmtWvXztDtHTlyRJLUu3dv1axZM0O3ndGqVatmdgkAADgMutYDABzapUuXNGjQIJUrV04FChRQ8eLF1bRpU23ZssXWJrWu9f/8849eeuklFS1aVL6+vmrXrp1OnTqVonv7hAkT5OHhocOHD+v555+Xv7+/ihYtqhEjRighIUFHjx5V69at5efnp4oVK2ratGkpajx37pz69Omj4sWLq0CBAqpRo4ZmzpyppKQku3apda3fu3evmjZtKm9vb5UuXVrjxo1TQkLCXZ+XFi1a6IUXXpAkNWzYUB4eHrau67frxt6iRQu1aNHC9vOPP/4oDw8PrVixQm+++aZKly6twoULq1WrVjp69GiK9X/44Qc99dRT8vf3V8GCBVWjRg1NmTJFkrEP5s6da3ucybfkywNSqyktz9uZM2fk4eGhGTNm6IMPPlBgYKB8fX3VuHFj7d27967PU0xMjEaNGqXAwEB5e3uraNGieuyxx7RixYoUbU+cOKG2bdvK19dX5cqV08iRIxUbG2vXJiIiQq+++qrKlCmj/Pnzq1KlSnrzzTft2j3//PMpPlhp3769PDw8tGrVKtuygwcPysPDQ+vWrbvr4wAA5CyckQcAOLS+ffvql19+0ZtvvqkyZcro6tWr+uWXXxQREXHbdZKSktShQwf9/PPPGj16tKpVq6a9e/eqTZs2t12nR48e6ty5s/r06aMtW7Zo+vTpSkhIUEhIiPr166dXXnlFK1as0NixY1W6dGm1bt1akvFBQ5MmTRQXF6dx48apWLFi+v777zV69GidOnVKM2bMuO19HjlyRK1atVLx4sU1d+5c5cmTR8HBwamGzP+aPn26vvzyS02ePFlz5sxR+fLlVbBgwbuul5o333xTdevW1UcffaSoqCiNHTvW9vw5OztLkhYtWqSXX35Zjz/+uGbOnKlChQrp+PHj+v333yUZlzfExMRo9erVCgkJsW27cOHCqd7nvT5vwcHBKleunN577z1J0ltvvaV27drpt99+k5eX120f28iRI7Vs2TKNGzdOVatWVUxMjH777bcUr5/4+Hh17NhRPXr00JAhQ7Rjxw5NmjRJXl5eGjVqlCTpxo0batmypU6dOqU33nhDlStX1s6dOzV16lT973//s4X0xo0ba/Xq1QoNDZW/v78SEhK0fft25c6dW1u2bFG7du0kGZdauLi46PHHH0/rrgIA5BAEeQCAQ9u9e7d69uyp3r1725Y9/fTTd1znhx9+0M6dOzVz5kz17dtXktS0aVO5urpq/Pjxqa7Tu3dvDRkyRJLUpEkTbd68WXPmzNGyZcv07LPPSpIaNGig9evXa/ny5bYgP2vWLF24cEHbtm2znYV94oknlJiYqE8++UQvv/yyypYtm+p9Tpo0SVarVd999538/PwkGWfNa9WqddfnpWLFiipZsqQkqVKlSqpRo8Zd17mdChUqaMGCBbafnZ2d1b17dx04cEC1a9fWtWvXNHLkSNWrV0/r1q2TxWKRZATWZKVKlbINGJeWSwju9XnLmzevvvrqK9sHC/7+/mrQoIF++OEHdejQ4bb3s2vXLjVt2lSDBw+2Lbu1V0KyuLg4vfHGG7aQ3bhxY/38889asWKFLcgvWbJEv/76qxYvXmxr17RpU3l4eGjs2LHavHmzmjZtanteQkJC1LVrV+3bt09RUVEaOnSoVq9ebbvPkJAQ1axZ09RxDQAAWRNd6wEADu2RRx7RkiVLNHnyZO3du1fx8fF3XWf79u2SZAtbyTp27HjbdVq2bGn3c/ny5WWxWPTkk0/alrm4uKh06dI6e/asbdm2bdtUsWLFFF2pn3/+eVmtVm3btu2297lt2zY1atTIFuIlI0Q/99xzd3h0Ga9Vq1Z2P1euXFmSbI9z9+7dioyMVL9+/Wwh/n7d6/PWokULW4hPrcbbqVmzpn744QeNHTtWP/74o65fv55qO4vFoqeeespuWeXKlVPsaw8PD7Vt2zZFzZK0detWScaHGsWLF7f1TNiyZYsqVaqkzp076/Tp0zp58qRiY2O1a9cuuw9DAABIRpAHADi0zz77TF27dtXChQvVuHFjFS1aVH379lVYWNht14mIiJCLi4u8vb3tlt9pirECBQrY/ezm5qY8efIoV65cKZbfuHHD7r5uDeLJ/P39bb+/U52prZvasgfpv8+Tu7u7JNlC7+XLlyUpQ0fcv9fn7XY13rovUjN16lS99tprWrt2rVq2bKmiRYuqU6dOOn78uF271Pa1u7u73favXLkiPz+/FB9m+Pr6ysXFxa7mRo0a2YJ9SEiImjRposqVK8vX11chISHatWuXrl+/TpAHAKSKIA8AcGgFCxbUlClTdOTIEf3xxx/6v//7P33zzTcaMGDAbdfx9vZWQkJCijB48eLFDK/P29s71e2GhoZKknx8fO553futM1euXCkGaZNuBvJ7lXzt/V9//XVfdd3qfp63e+Hh4aExY8bo4MGDOnnypGbMmKG9e/fesTv+7fj4+Cg8PFxWq9VueXh4uBISEuxqbtSokS5cuKD9+/dr3759atKkiSRjYMItW7YoJCREefPmzfCZDAAA2QNBHgCQbQQEBOjFF19UkyZN9Msvv9y23WOPPSZJ+uqrr+yWf/nllxleU6NGjXTkyBEdPHjQbvnSpUtlsVjUoEGD267bsGFDbd261S7QJiYmpqj7XhUrVky//fab3bJjx47p2LFj6dpe3bp15eXlpfnz56cIsbdyc3OTpNt2X7/V/Txv6eXn56fu3burQ4cOOnr0qGJiYu5p/UaNGunatWv69ttv7ZYvXbrU9vtb21osFr311ltycnKyvSYbN26sH3/8UVu2bFH9+vXl6up6fw8KAJAtMdgdAMBhXb16VS1btlTHjh1Vvnx55c2bVwcOHNDGjRttA9Cl5sknn1S9evU0atQoRUZGqnr16tq7d68tcDk5Zdzn3IMGDdLSpUv13HPPaezYsQoICND333+v4OBg9evX77YD3UnS8OHD9d1336lVq1YaOXKk8uTJo7lz5yo6Ovq+aurSpYteeOEFvfrqq2rdurXOnj2rGTNmpHtU+7x58+rdd9/VwIED1apVK/Xu3Vu+vr46efKkDh8+bJuSr1KlSpKkadOm6cknn5Szs7MqV65sC/i3up/n7V40bNhQLVu2VOXKlZU/f379+eef+uKLL1SnTh3lyZPnnrbVtWtXzZ07V/3799eZM2dUqVIl7dq1S1OmTFHz5s1tZ90lo7t9YGCgNm/erAYNGtjuq0mTJoqIiFBERIQmTZqUIY8RAJD9EOQBAA4rV65cqlWrlpYtW6azZ88qPj5eAQEBeu211zR06NDbrufk5KQvv/xSo0aN0rRp0xQXF6e6detq/vz5atSo0R2nK7tXhQoV0pYtWzRu3DiNHz9ekZGRKlmypN555x3bKPi3U6lSJa1du1ajRo1S//79lT9/fnXp0kVt2rTRoEGD0l1Tp06dFBoaqvnz52vx4sUKDAzUjBkz9O6776Z7mz179lThwoU1ffp0vfzyy7JarSpevLi6du1qd7+7d+9WcHCw3n33XVmtVv3+++8qXrx4iu3dz/N2Lxo2bKjvvvtOH374oWJiYlSkSBF16dJFw4cPv+dt5cqVS+vXr9f//d//acaMGbp8+bKKFCmiV155RaNHj07RvnHjxvrtt9/sAn5AQIDKlCmj48ePc308AOC2LNHR0bfvAwcAQA6yfPly9enTR5s3b1bdunXNLgcAACBVnJEHAORIK1as0IULF1SpUiU5OTlp3759mjFjhh577DFCPAAAyNII8gCAHClfvnxauXKl3nvvPUVHR6tw4cJ6/vnnNW7cOLNLAwAAuCO61gMAAAAA4ECYfg4AAAAAAAdCkAcAAAAAwIEQ5AEAAAAAcCA5brC7pKQkhYaGKm/evLJYLGaXAwAAAADI5qxWq65duyZ/f385Od3/+fQcF+RDQ0NVrlw5s8sAAAAAAOQwR48e1UMPPXTf28lxQT5v3rySpHPnzsnT09PkagAAcBxhYWH69NNP1bt3bxUuXNjscgAAcBiRkZEKCAiw5dH7leOCfHJ3ek9PT4I8AAD3IDo6Wrly5VK+fPn4GwoAQDpk1OXdDHYHAAAAAIADIcgDAAAAAOBACPIAAAAAADiQHHeNfFpYrVYlJCQoMTHR7FKALMPZ2VkuLi5M2wgAAACYjCD/H3FxcQoNDVVMTIzZpQBZTp48eeTv7y83NzezSwEAAAByLIL8LZKSknTq1Ck5OzurSJEicnNz4+wjIKOXSlxcnC5duqRTp06pbNmycnLiyhwAAADADAT5W8TFxSkpKUkBAQHKkyeP2eUAWUru3Lnl6uqqM2fOKC4uTrly5TK7JAAAACBH4pRaKjjTCKSO9wYAAABgPv4rBwAAAADAgRDkc4BevXqpTZs2ZpchSSpRooRmzJhxxzYWi0Vr1qzJlHru144dO1SlShW5urqa/hxnpf0MAAAA4MHhGvkcYObMmbJarWaXIUnat2+fPDw8zC4jw7z22muqVq2a1q9fr7x582bKfZ4+fVolS5bUwYMHVa1aNdvyrLSfAQAAADw4BPkcwMvLy+wSbAoVKmR2CSnExcWlezq1EydO6MUXX1TRokUzuKp7l5X2MwAAAIAHh6712cTKlStVpUoV5c6dWz4+PmrWrJmio6MlpexyHRUVpW7dusnDw0P+/v6aPn26GjVqpFdffdXWpkSJEnrnnXfUo0cP5c2bV8WLF9fXX3+tS5cuqXXr1sqbN6+qVKmi/fv329Xx1VdfqVKlSnJ3d1eJEiX0/vvv2/3+v13rjx07pgYNGihXrlwKDAzUxo0b7/pYk5KSNHnyZJUpU0bu7u4qVqyYJkyYYPv94cOH1aRJE9tz0b9/f127ds32++Tn491331WRIkVUrlw5SdJff/2lTp06qUCBAvLx8VHr1q11+vTpVGs4ffq0LBaLrly5oj59+shisWjhwoVauHCh8ufPb9d2zZo1dtMYvvnmm6pWrZoWL16sEiVKyMvLS507d1ZUVFSaHmPJkiUlSdWrV5fFYlGjRo3sHley2NhYDRkyRL6+vsqVK5cee+wx7du3z/b7rVu3ymKxaPPmzapZs6by5MmjRx99VH/++edd9wEAAAAA8xDks4HQ0FB16dJFffr00ZEjR7R161a1a9futt2sX3vtNe3YsUPffPONNm7cqJ9++kk///xzinbTp09X/fr1dfDgQbVq1Urdu3dXjx499Pzzz+vnn39WmTJl1KNHD9v9HDhwQB07dlTnzp11+PBhvfnmmxo7dqwWLlyYah1JSUlq166dnJ2dtXv3bs2ZM0cjRoy46+MdNWqUJk+erLFjx+r333/X0qVL5efnJ0mKiYlRixYtVKBAAe3bt09ffvmlNm3apEGDBtltY/PmzTpy5Ig2btyotWvXKiYmRo0bN1bevHn1448/avv27cqbN69atGihuLi4FDUEBAQoNDRUnp6emjFjhkJDQ9WpU6e71p7sxIkTWrNmjdauXau1a9dq27ZtmjRpUpoe4969eyVJmzZtUmhoqFatWpXqfQwfPlxfffWVFi1aZNtfzZs3V0REhF27N954Q++//772798vFxcX9enTJ82PAwAAAEDmo2t9GsTESH/8kfn3W6GClJbp7ENDQ5WQkKB27dqpePHikqQqVaqk2jYqKkqLFi3S0qVL1bRpU0nSp59+qiJFiqRo+9RTT2nAgAGSpHHjxmn27NmqVauWOnToIEkaMWKE6tWrp4sXL6pw4cKaNm2amjZtqrFjx0qSypUrp99//11TpkxRr169Umx/06ZNOnLkiE6fPm3rmj5x4kS1bNnyto81KipKM2fO1IcffqiePXtKkkqXLq3HHntMkrRkyRJdv35dn332me1a/A8//FDPPPOMJk+ebAvDHh4e+uSTT2xd6hcsWCAnJyd98skntrPnn376qfLnz6+tW7fqySeftKvD2dlZhQsXlsVikZeXlwoXLnzbmlOTlJSkhQsXKl++fJKk7t27a/PmzZowYcJdH2Py5Qk+Pj63vd/o6GjNnj1bCxcutD2f8+bN08aNGzV//nwNGzbM1nbChAlq2LChJGnkyJFq1aqVbty4wTzxAAAAQBZFkE+DP/6QHnkk8+/3wAGpRo27t6tataqaNm2qKlWqqHnz5nryySfVvn17FShQIEXbkydPKj4+XrVr17Yt8/LyUvny5VO0ffjhh23fJwfgWz8gSF4WHh6uwoUL68iRI2rdurXdNurXr68ZM2YoMTFRzs7Odr87cuSIihUrZnd9eb169e74WI8cOaLY2FjbhxCp/b5q1ap2A+rVr19fSUlJ+vPPP+0ex63XxR84cEDHjx+3BetkN27c0IkTJ+5YU3qUKFHC7r78/f0VHh5uewx3eoxpceLECcXHx6t+/fq2Za6urqpdu7aOHDli1/bW/ezv7y/J2KfFihVL9/0DAAAAeHAI8mlQoYIRqs2437RwdnbWxo0btXPnTv3www+aNWuW3njjDe3Zs8d2PXWy5G7wt16zfevyW7m6utq+T26f2rKkpCTbNtKy3Tv97r/r/1fu3Lnv+PvUakht2/8dOT8pKUmPPPKIlixZkmK9exmgz8nJKcXjio+PT9Hu1ucxubbk5/FujzEt7rSf/7vsTvsUAAAAQNZDkE+DPHnSdmbcTBaLRfXr11f9+vU1btw4FS9eXKtXr9Zrr71m16506dJydXXV3r17FRAQIEmKjIzUsWPHbN2r0yswMFDbt2+3W7Zz506VK1cuxdn45PZnz57VhQsXbF37d+3adcf7KFu2rHLnzq3Nmzerb9++qW5z0aJFio6OtoX1HTt2yMnJyTaoXWpq1Kih5cuXy9fXV56ennd9rLdTqFAhRUVF2d3/L7/8ck/buNtjTO5JkJiYeNttlClTRm5ubtq+fbu6du0qyfhAYf/+/XaDGgIAAABwPKYOdrd9+3a1b99epUuXloeHh7799tu7rvPTTz+pfv368vb2VqVKlfTJJ59kQqVZ2549ezRx4kTt379fZ8+e1apVq3Tp0iVVrFgxRdt8+fKpZ8+eGjZsmEJCQvTbb7+pT58+cnJyuuvZ8Lt5/fXXtXnzZr399ts6evSoFi1apA8//FBBQUGptm/WrJnKly+vHj166NChQ/rpp5/0xhtv3PE+cuXKpREjRmj48OH67LPPdOLECe3evVvz58+XJHXr1k25cuVSz5499euvvyokJESDBw9W9+7dbd3qU9OtWzcVLFhQrVu31k8//aRTp05p27ZteuWVV3T+/Pk0Pwd16tRRnjx5NHr0aB0/flxLly697WB/6X2Mvr6+yp07t77//ntdvHhRV69eTbENDw8PvfTSSxo2bJi+//57/f777+rXr59iYmL0wgsv3FM9AAAAALIWU4N8dHS0qlSpomnTpqWp/enTp9WuXTs9+uij2rlzp4YNG6agoCCtWbPmwRaaxXl6eurHH3/UU089pXLlymnMmDF6//33bzto3LRp01SvXj09/fTTatasmerXr6+KFSve9+BmNWrU0IoVK/TFF1+ocuXKGjdunN56661UB7qTjG7oq1evVmxsrGrXrq2+ffvaTSN3O2PHjtXrr7+ucePGqWLFiurUqZPt+vI8efJow4YNioiIUK1atdS+fXs1bdpUH3744R23mSdPHv34448qVqyY2rVrp4oVK6pPnz66fv36PZ2h9/b21ueff65169apSpUqWrZsmd588800r5+Wx+ji4qIPPvhAc+fOVZEiRVKMS5Bs0qRJeu6559S9e3fVqFFDx48f14YNG1IdOwEAAACA47BER0ff/iLmTOTh4aEvvvhCzzzzzG3bjBkzRuvWrbObKm3IkCE6fPiwQkJC0nQ/kZGR8vf319WrV20BLT4+XlarVQkJCTpz5oxKliwpd3d323XGTk43P++wWq2264yTz2AnL8sqbVNbfqe2MTExeuihhzR16lTbnOi3np1Pvl76bts1q+1/n5+s0DY7vE5Se8w3btzQyZMnVbRoUeXJk0cuLjevzkmeps/V1dW2jcTERCUmJsrJySndbZPfny4uLrbHl5SUpISEBFksFrtr/LNC24SEBCUlJcnZ2dl2Scm9tLVarbZxFW4dkDEj26b2vN9L2/vZn/e777Pz6yQz9v39vk7Cw8M1f/589e/fX/7+/g9s33OMyHr7nmOE+a8TRzhGZNa+5xiR8fuTY8SD3/fXrl2Tl5eXbQrr++VQ18jv3btXTZo0sVvWrFkzLVq0SPHx8SkGEJOk2NhYxcbG2n6OiopK0WbJkiU6c+aM2rVrZ9uhcXFxunLlipydne26ZEdERCg2Nlb58+dXnn/nhktISNClS5fk5ORkNx3Y33//rRs3bsjLy8t2vXTyP0IWi8U2Qrgk/fPPP7azv3nz5pVkvCAuXrwoSXbTw129elUxMTHKly+fbeRzq9WqsLAwSbLbbmRkpO16bS8vL0nSwYMHtXv3blWrVk1ubm565513bM9lWFiY8uTJo/z589u2kbxdPz8/2xs0OjpakZGRyp07t90Z3osXL8pqtcrX19f2XMbExOjq1avKlSuXvL29bW3Dw8OVlJSkQoUK2fbd9evX9c8//8jd3V0+Pj62tpcuXVJiYqJ8fHzk7u4uyRhR/u+//5abm5sKFixoa3v58mUlJCTI29vb1ssgNjZWERERcnV1tRu8LiIiQnFxcSpQoIBtkLnkfe/i4iJfX1+7/fnffR8fH6/Lly+neJ2ktu9v9zpJbd/f7nWS2r6/3esked/nzZvXdrC49XWSPH2eZLwvrl27Zvc6ud2+j42NVXBwsMqVK6dnn33W1nbq1KmKj4/XK6+8Ynv97Nu3Txs2bFCVKlXUrl07W9uZM2cqJiZGL730ku05/uWXX7R27VqVL19enTt3trX96KOPdPXqVfXt21cPPfSQJOnXX3/V6tWrVapUKXXv3t3Wdt68ebp06ZJ69uypEiVKSJKOHj2q5cuXKyAgQH369LG1XbhwoS5cuKAuXbrYxk84deqUPv/8c/n5+enFF1+0tU0+RrRv316VKlWSJJ0/f16ffvqpvL29NXjwYFvbFStW6NixY2rdurWqVasmyXitz507V/ny5bMbt2L16tX6/fff1bJlS9tMEhEREfrwww/l7u6ukSNH2tquXbtWhw4dsvWiSd5v06dPl5OTk23aR0nasGGD9u/fr4YNG6pRo0a2/TZ58mRJxoeiyftz8+bN2rVrl+rVq2ebZjEpKUnvvvuuJGOayeT30U8//aRt27apZs2aatWqle3+Jk+erKSkJA0dOtT2Wtu9e7c2bdqkqlWrqk2bNra206ZNU2xsrAYNGmR7jx84cEDr169XYGCgbXpLSZo1a5aioqI0YMAA23vm8OHD+vrrr1W2bFnb+A+SNGfOHEVERKh37962GReOHDmilStXqnjx4nY9g+bPn6+LFy/q+eefV+nSpSVJx48f17Jly1SkSBH169fP1nbx4sU6d+6cOnXqpAr/jkB69uxZLVq0SIUKFdLAgQNtbb/44gudPHlSbdu2tc0GERoaqk8++UReXl5241OsXLlSf/75p55++mk98u+0KJcuXdLs2bOVJ08euykiv/nmGx0+fFjNmzdX3bp1JRnHgpkzZ8rV1VWjR4+2tV23bp0OHjyoxo0bq0GDBpKMY/DUqVMlSePHj7e13bRpk/bs2aPHHnvMNktGfHy8bd+PGjXK9o/d1q1btX37dlWuXFm3Sm4bFBRkNy5JSEiIqlevzjGCY4QkjhHJcsIxok6dOmrRooVtG456jOjRo6eKFSuhpCTpjz+OatWq5XrooQB17dpHVqtktUqff75QFy9eUOvWXVSyZDlZrdKZM6e0Zs3nKljQT506vWhru2bNEoWGnlGzZu1VsmQlWa1SWNh5rV37qfLl89Zzzw22td28eYX++uuY6tZtrVKlqkmSIiLC9f33c5U7dz4988xrtra7dq3WX3/9rqpVW6pkydqyWqWoqAht2fKhXFzc1bz5SFvbQ4fW6sKFQypfvplKljSOEdevR2nbtumyWJz05JNjlTxe85EjG3Tu3H6VKtVQpUs3+nffx2rrVuMY0aTJGDk5GceIY8c268yZXSpWrJ7KljWOEYmJSdq61dj3jz8+Qi4uxjHi1KmfdPr0Nj30UE2VLXvzGLFt22RZrUmqW3eo3N2NY8S5c7t18uQm+flVVfnybSQZj2PnzmlKTIxVzZqDlDu3j6xW6cKFAzp5cr18fAJVocLNY8S+fbMUFxelqlUHyMPDOEaEhx/W8eNfK3/+sqpY8eYx4uDBObpxI0KVKvVWvnzFZLVKV64c0fHjK5UvX3EFBvayPT+//jpfMTEXVa7c8/LyMo4R//xzXMeOLVOePEUUGHjzGHHmzGJdumQcI1Kb7vt+OFSQv3jxYorrnH19fZWQkKDLly/bBZ5kU6dO1cSJEzOrRIcxZ84cnThxQu7u7nrkkUf0008/ycfHJ9UPOgAAAJD9Xb0qxcUZt+QheMLDpX37jGXXr99su2aNFB8vJSRIly8byw4dMqZtTkgwbsnefffmMhcXKXduaft26euvby4vU0ZycpL69ZNiYoxlfn5S6dLSxo3S9OlSYqKUlCQ1aSK5u0vt2xt1JiVJxYtLtWpJmzZJb7xhLEtKkjp0kPLlk1q0kC5eNJaVKSO1bClt2SINGHCzbf/+UqFCxvZPnzZqr1BB6txZ2rXLqC1Zv37SQw9JHTtKx44Zy0qVknr0kH79VRo06GbbXr2kEiWM7f/+u7EsIEB64QXjfv79XFGS1LWrVK6cNHKklDxecuHC0osvGvUHBt5s26GDVKmSNHGisY8kydtbGjJEunbNeD6StWkjVasmzZol7dxpLMuXT3r9deO5vnUG6KeekmrXlhYskLZuNZblymXUJEmNGhnPlyQ98YRUv760bJmxnyRjP44bZ3zfqpV048bN9Ro1klavltatu3l/Y8dKzs7G40mOIo8+Kj35pLRhg/TSSzfbjhxp1NKjhxQRYSyrVcu4nx9/lG753FSvvSZ5ehrr/3tuStWqGc/F3r3SreM/Dx4s+fgY65w7ZywLDDT27+HDxvOU7MUXjX0yZox08qSxrGxZqVs347UwfPjNtm+9pQfGobrWV61aVc8//7zdp5C7du1Ss2bNdOLECbuznMlSOyNfrlw5utbfR/fqrNb2v89PVmibHV4nqT1mutbTJS4nd4mj2yxd6zlGcIzIzNdJQkKSrl93VkyMsyIjpchIq65di9f161JcnJtiYoxgHR2doOvXjbZGe+n6dauuX4/XjRvStWtuun7daHvjRoJiY5MUHe2sGzecFRcnxcZa5eQU/2+NN18nzs4JcnJKUlKSsxITk2cfssrVNbmtqyTLv20T5eqaKGdnJ1ksLnJxMQJ7rlxxMnaDq1xcLHJxkVxdE+XmZrR1dr7Z1s3NaOvkdLOts3OiXFwS/x2U2UVOTkbgc3aOk5OT0dbJyfLv94lydjbaOjndbOvkFC+LxSpnZxc5OzvJyUmyWJL+fXwWOTu72tpaLEZbFxeXfx+L0VYy9pGzs+u/yySrNV6S9d/7MtpKd27r7GzfNinJaOvicmvbBElJcnIy3nPJba3WlG0TE422ye9Po61VSUnxslgkV1c3W9ukpJvbTT6bbrUabSXJxcXY98nbtVpv1pDcNjHR2K7x2G6+P6VEWSw320pGW+O1Yeyj5LZWq7GPnJ1vvj8TEuJSbDcpyWhrsRhtk/89jY9PeYxISko+TtlvNzHReM/d+rwnt7VYnOTqemsNqb8/b91Hyc9Pctvk11Ry28TElO/lXLnilScPXevl5+dn60Kc7NKlS3JxcbHrhn0rd3d3W1fs20l+sm+dO/u/geZOy7NzW8k+HNI2bW2z6v7MqH3v5uZm9w+SZP9PYrJb//FLb9vULplxcnJKdRtZoe1/n5d7bZv8/GZW29Se93tpK2Xuvs/Or5PM3vfpeZ3897nPqq8TR9v3Wfl1wjEifW1dXNwUGSn9/bdx1tC4udq+j4w0zjxGRTkpMtLt3+9vXe6ia9f+u2WLpJQ15M7tojx5jLPcN79alDu3m3LnlgoUkIoUSf6di3LnNs5oursbNzc3i9zd3eTmJrm5JS+T3N1dUllm7Ptbl7m66t8QmfJ5T61eyfnfW2a1TbmPjPG+U9tGVmibWjy7l7apv04eXNvUnvd7aasH2Da15z0rvE4yhkMF+dq1a2v9+vV2yzZv3qwaNWqkeiAFAAAA7ofVagTsixeNW3j4za9XrhjB3D6wGz/fcn7IxtnZCNZeXka3Zk9P46ufn9E1N18+++X//T5PHtmFdnd3KZXP4QHkAKYG+WvXrunEiRO2n0+fPq1Dhw7J29tbAQEBGjdunC5cuGCbK75v376aO3euRowYod69e2vPnj1atGjRPc/TfTfJXY8B2OO9AQDILqxW4/rqv/6Szp83bsnfX7hgH9xvuUpTkhHIfX2lggWNa5ILFDCuVfb2Tv1WoIDxNV8+gjeAjGFqkP/555/t5jpPHn21W7duCg4OVlhYmM6fP2/7fYkSJbRq1SqNGDFCwcHB8vf319SpU+1GO70fyWf1Y2JibCOYA7gpJiZGUupdCQEAyEqSkowBrk6dunk7eVI6e/ZmaI+Otl/Hz08qWtToil69uhHW/fxufk3+vkABY0AvADCLqUG+QYMGiv7vEfQWwcHBKZY9/vjj2pk81GIGc3Z2Vv78+RUeHi5JypMnT6rXDQM5jdVqVUxMjMLDw5U/f/5Urz8EACCzJSVJZ84YI6X/8Yd04oQR1k+dMkYDTx4tWzJGIy9Z0hjdvFo1Y8TxokVvfvX3N675BgBH4FDXyGeG5JHvk8M8gJvy58+f6uwQAAA8SNevS3/+eTOw//GHdOSIdPTozbCeO7cxVVnJklLz5sbXkiWNKcFKlJDy5jX1IQBAhiLI/4fFYpG/v798fX1tU6sAMLrTcyYeAPCghYcb82cfPHjz69GjxjXtktG1vWJFY97r3r2N7ytUMOblprs7gJyCIH8bt5u+BAAAABnj3Dlp71770H7hgvG7vHmlqlWlJ56QgoKMweTKlzcGjQOAnI4gDwAAgAcuPl46dEjaudO47dhhDDonSYULG4PL9expfK1Wzegmzxl2AEgdQR4AAAAZ7p9/bgb2nTuNM+8xMcaAcrVqSV26SI8+KtWtawR5AEDaEeQBAABw3+LjpT17pI0bpR9+MIJ7UpJxTXv9+tJbbxnBvUYNyd3d7GoBwLER5AEAAHDPrFZjurcffjBuW7ZIUVHGHOtPPCH17Ss1amSMGs9svgCQsQjyAAAASJPYWCOwf/ONtGGDMV+7i4txpn3ECOnJJ40z7owXDAAPFkEeAAAAt3X1qrRunbRmjfH12jXjLHurVkZwb9RIypfP7CoBIGchyAMAAMDOtWvGWffly6Xvv5fi4qSaNY2z7m3aGFPB0V0eAMxDkAcAAIDi4owz7kuWSGvXSjduGCPKT54sPfecFBBgdoUAgGQEeQAAgBzKapV+/llatEhatky6fNmYx/3//k/q2FEqUcLsCgEAqSHIAwAA5DD//CMtXiwFB0u//mrM496rl9Szp1S5stnVAQDuhiAPAACQA1itxtzuc+YY177Hx0utW0vvvWdMF+fCf4UA4DA4ZAMAAGRjsbHSihXSjBlGN/oSJaQxY6Q+fYwz8QAAx0OQBwAAyIbCw6W5c6WPP5bCwqSWLY3B7Jo3l5yczK4OAHA/CPIAAADZyMmT0pQp0qefGoG9Rw/plVekihXNrgwAkFEI8gAAANnAb79JkyYZo897e0tjx0ovvij5+JhdGQAgoxHkAQAAHNj//ie9+aa0erUx1/v06dILL0h58phdGQDgQeEKKQAAAAf0xx9S585S1apGmJ8/Xzp+XBo8mBAPANkdQR4AAMCBnDplzPleqZK0c6c0b5505IgxCr2bm9nVAQAyA13rAQAAHMA//0jvvCPNmmVcAz9zptSvn+TubnZlAIDMRpAHAADIwuLjpdmzpf/7P+nGDWn0aCkoSPLwMLsyAIBZCPIAAABZ1Pr10quvSseOGV3n335b8vc3uyoAgNm4Rh4AACCLOX1aattWeuopqWhR6ZdfpE8+IcQDAAwEeQAAgCwiNlaaMEEKDJT27pWWL5c2bZIeftjsygAAWQld6wEAALKAH380Bq87eVIaOlQaO1bKl8/sqgAAWRFn5AEAAEwUGSkNHCg1bCgVKiQdOiS99x4hHgBwe5yRBwAAMMl330kvvmhMLffhh9JLL0lOnGYBANwFfyoAAAAy2dWrUs+e0tNPS5UqSb/+Kr38MiEeAJA2nJEHAADIRNu2ST16GGfhP/3UCPQWi9lVAQAcCZ/7AgAAZILYWGnYMKlxY6lECel//5N69SLEAwDuHWfkAQAAHrDffpO6dJH+/NMYyG7oUMnZ2eyqAACOijPyAAAAD4jVanSfr1VLSkqS9u2TgoII8QCA+0OQBwAAeACuXTOuf+/TR+raVdq7V3r4YbOrAgBkB3StBwAAyGCHD0sdO0rnzkmffy5162Z2RQCA7IQz8gAAABlo6VKpTh3JzU06cIAQDwDIeAR5AACADJCQIL32mhHc27eXdu+Wypc3uyoAQHZE13oAAID7dOmS1KmT9OOP0gcfSIMGMa0cAODBIcgDAADch4MHpTZtpOvXpc2bpYYNza4IAJDdmd61Pjg4WIGBgfL29lb9+vW1Y8eOO7b/4osvVKdOHRUsWFClSpXSgAEDdOXKlUyqFgAA4Kavv5Yee0zy9TWuhyfEAwAyg6lBfuXKlRo+fLiGDx+unTt36tFHH1Xbtm117ty5VNvv3LlT/fr1U8+ePbV//359/vnnOnDggF5++eVMrhwAAORkVqv0/vtS27bSU09J27ZJAQFmVwUAyClMDfKzZs1Sz5491atXL1WoUEFTpkxR0aJFNW/evFTb7927V8WLF9fAgQNVokQJPfroo3rhhRf0888/Z3LlAAAgp4qPl158UQoKkkaOlJYvl/LkMbsqAEBOYlqQj4uL08GDB9W0aVO75U2aNNGePXtSXadu3br666+/9P3338tqterixYtas2aNWrRokRklAwCAHO7qVeMM/KefSgsWSBMnSk6mX6gIAMhpTPvTc+XKFSUmJsrX19duuZ+fny5evJjqOnXr1tWCBQvUs2dP5c+fX6VKlZKXl5fef//9295PbGysIiMjbbeoqKgMfRwAACBnuHBBatBA2r9f+uEHqXdvsysCAORUpn+GbPnP3CxWqzXFsmRHjhxRUFCQRo4cqe3bt2vNmjU6ffq0hgwZctvtT506Vf7+/rZbuXLlMrR+AACQ/f35p/Too1JEhLR9u9SokdkVAQByMtOmn/Px8ZGzs3OKs+/h4eEpztInmzp1qurVq6ehQ4dKkqpUqSIPDw898cQTGjdunPz9/VOsExQUpMGDB9t+joqKIswDAIA027NHatXKGJl+wwYGtQMAmM+0M/Jubm6qXr26tmzZYrc8JCREderUSXWd69evy+k/F6I5Ozvf8X7c3d3l6elpu+XLl+/+CgcAADnG+vVSkyZS+fLGmXhCPAAgKzC1a/3gwYO1cOFCLVq0SH/88YeGDx+uc+fOqW/fvpKkcePG2b6XpJYtW+rrr7/WvHnzdOrUKe3atUtBQUGqWbNmqmfjAQAA0uvLL6Vnn5WaNpU2bpS8vc2uCAAAg2ld6yWpffv2ioiI0KRJkxQWFqbAwECtWrVKxYoVkySFhYXp/Pnztvbdu3fXtWvXNHfuXI0aNUpeXl5q2LCh3nnnHbMeAgAAyIY++8wYzK5zZ2nhQsnV1eyKAAC4yRIdHW01u4jMFBkZKX9/f129elWenp5mlwMAgMMIDQ1VcHCw+vfvn617ws2eLQ0cKPXtK82ZI93lKj4AAO4qMjJSXl5eCg0NzZAcavqo9QAAAFnF++8bIf6VV6TgYEI8ACBrIsgDAABImjBBCgqSRo+Wpk+XbjMbLgAApiPIAwCAHG/iRGnMGOmtt4xAT4gHAGRlBHkAAJCjTZ4svfGG9H//J40da3Y1AADcHUEeAADkWFOmSCNHSuPHS+PGmV0NAABpQ5AHAAA50vvvS8OHG2fhx483uxoAANKOIA8AAHKcjz++ObDd//0f18QDABwLQR4AAOQon30mvfyy9Npr0jvvEOIBAI6HIA8AAHKMVauk3r2lvn2lqVMJ8QAAx0SQBwAAOcKGDVLnzlKHDtKcOYR4AIDjIsgDAIBsb/t2qW1b6cknpcWLJWdnsysCACD9CPIAACBbO3xYevppqU4d6csvJVdXsysCAOD+EOQBAEC2deaM1KKFVLKk9PXXUu7cZlcEAMD9I8gDAIBs6coVqXlzyd1dWr9e8vQ0uyIAADKGi9kFAAAAZLToaKM7/ZUr0s6dUuHCZlcEAEDGIcgDAIBsJSFB6tTJuDY+JEQqW9bsigAAyFgEeQAAkG1YrdLAgcZUc99+K9WqZXZFAABkPII8AADINiZPlubNkxYsMAa5AwAgO2KwOwAAkC2sWCGNGiWNGSP17m12NQAAPDgEeQAA4PB27pR69JC6dpXeesvsagAAeLAI8gAAwKGdOCG1bi3Vrm10qbdYzK4IAIAHiyAPAAAcVkSE9NRTkre3tGaNMWc8AADZHYPdAQAAhxQfL3XsKF2+LO3ZY4R5AAByAoI8AABwSK++Km3bJm3cKJUpY3Y1AABkHoI8AABwOB9/bNyCg6VGjcyuBgCAzMU18gAAwKFs2iQNGSK98orUr5/Z1QAAkPkI8gAAwGEcPSp16CA1ayZNnWp2NQAAmIMgDwAAHEJkpDHNnJ+f9MUXkgsXCAIAcij+BAIAgCwvKUnq2VO6cEHat0/Kn9/sigAAMA9BHgAAZHmTJhnzxH/9tVSunNnVAABgLrrWAwCALO3776UxY6Rx46RnnzW7GgAAzEeQBwAAWdbJk1LXrtJTT0njx5tdDQAAWQNBHgAAZEnR0VLbtpK3t/T555IT/7UAACCJa+QBAEAWZLUac8QfPy7t2cPgdgAA3IogDwAAspwZM6Rly6Tly6XKlc2uBgCArIVOagAAIEsJCZGGDZOCgqSOHc2uBgCArIcgDwAAsoxz56ROnaRGjaR33zW7GgAAsiaCPAAAyBJu3JDatZNy55a++EJy4QJAAABSxZ9IAACQJQwaJB0+LO3YIRUsaHY1AABkXQR5AABguk8/lebPN74+8ojZ1QAAkLXRtR4AAJjq11+ll1+WXnhB6tXL7GoAAMj6TA/ywcHBCgwMlLe3t+rXr68dO3bcsX1sbKzefPNNVahQQQUKFFDlypW1aNGiTKoWAABkpGvXpA4dpDJlpFmzzK4GAADHYGrX+pUrV2r48OGaMWOG6tatq/nz56tt27Y6cOCAAgICUl2ne/fuCg8P18cff6zSpUvr0qVLSkhIyOTKAQDA/bJapQEDpPPnpf37jUHuAADA3Zka5GfNmqWePXuq17/96KZMmaLNmzdr3rx5euutt1K0/+GHH7R9+3b9+uuv8vb2liQVL148M0sGAAAZZN48aelS41a+vNnVAADgOEzrWh8XF6eDBw+qadOmdsubNGmiPXv2pLrOunXrVL16dU2fPl1lypRR1apVNWrUKF2/fv229xMbG6vIyEjbLSoqKkMfBwAAuHe//CINGSK9+KLUpYvZ1QAA4FhMOyN/5coVJSYmytfX1265n5+fNm3alOo6p06d0q5du5QrVy598cUXunz5soYOHaq///5bc+bMSXWdqVOnauLEiRlePwAASJ/ISOO6+MBAafp0s6sBAMDxpDnIf/fdd2neaKtWrdLc1mKx2P1stVpTLEuWlJQki8WiBQsWyMvLS5Jxxr1bt26aPn26cqdycV1QUJAGDx5s+zkqKkrlypVLc30AACDjWK1Sv37SxYvS+vVSrlxmVwQAgONJc5Dv1KmT3c8Wi0VWq9Xu52Rp6b7u4+MjZ2dnXbx40W55eHh4irP0yQoXLqwiRYrYQrwklS9fXlarVX/99ZfKlCmTYh13d3e5u7vftR4AAPDgzZ4trVghffmlMVI9AAC4d2m+Rv7atWu22zfffKOHH35Yq1ev1oULFxQaGqpVq1apWrVqWrNmTZq25+bmpurVq2vLli12y0NCQlSnTp1U16lXr55CQ0N17do127Ljx4/LyclJDz30UFofCgAAMMGBA9LQodLgwVL79mZXAwCA40rXYHfDhw/XlClT9MQTT8jT01P58uXTE088oUmTJmnYsGFp3s7gwYO1cOFCLVq0SH/88YeGDx+uc+fOqW/fvpKkcePG2b6XpI4dO8rb21svvviijhw5ou3bt+uNN95Qjx49Uu1WDwAAsoarV6WOHaWqVaUpU8yuBgAAx5auwe5OnTolT0/PFMs9PT115syZNG+nffv2ioiI0KRJkxQWFqbAwECtWrVKxYoVkySFhYXp/PnztvZ58+bVt99+q9dff12PP/64vL291a5dO40fPz49DwMAAGQCq1Xq00eKiJA2bZK44g0AgPtjiY6Ott69mb0nn3xSLi4umj9/vvz9/SUZobtv376Kj4/Xhg0bMrzQjBIZGSl/f39dvXo11Q8jAABA6kJDQxUcHKz+/fvb/v6nxYcfGt3pV6+W2rR5cPUBAJBVRUZGysvLS6GhoRmSQ9N1Rn727Nnq3LmzKlasqICAAEnSuXPnVKZMGS1fvvy+iwIAANnDoUNSUJAxZzwhHgCAjJGuIF+6dGnt3btXmzdv1tGjR2W1WlWhQgU1adLktlPHAQCAnCU6WurUSapYUXrvPbOrAQAg+0hXkJeM6eaaNWumZs2aZWQ9AAAgmxgyRDp/3hitnuviAQDIOGkO8h9//LH69OmjXLly6eOPP75j24EDB953YQAAwHF98YW0YIH06adS+fJmVwMAQPaS5iD/4YcfqlOnTsqVK5c+/PDD27azWCwEeQAAcrCTJ6X+/aWuXaWePc2uBgCA7CfNQf73339P9XsAAIBk8fFSly6Sr680e7bE0DkAAGS8dF8jn8xqNWavY5A7AAAwZoz088/Szp0Ss7wCAPBgOKV3xSVLlqhWrVry8fGRj4+PateuraVLl2ZkbQAAwIH88IMxOv3EiVKtWmZXAwBA9pWuM/IffPCB3n77bQ0YMED16tWT1WrVrl279Morr+jKlSsaPHhwRtcJAACysIsXpR49pObNpddfN7saAACyt3QF+Tlz5mjGjBnq1q2bbdnTTz+tihUrauLEiQR5AABykKQkI8RL0qJFklO6+/sBAIC0SFeQDwsLU926dVMsr1u3rsLCwu67KAAA4Djef9/oVr9hg+TnZ3Y1AABkf+n6zLxUqVJatWpViuVfffWVSpcufd9FAQAAx7B3rzR6tDR8uPTkk2ZXAwBAzpCuM/JjxoxRjx49tH37dtWrV08Wi0U7d+7U1q1btXjx4oyuEQAAZEGRkcZUczVqSO+8Y3Y1AADkHOkK8m3atNG2bds0a9Ysffvtt7JarapQoYK2bdumatWqZXCJAAAgq7FapZdeki5dkjZulFxdza4IAICcI93zyFevXl0LFizIyFoAAICDWLRIWrrUuJUqZXY1AADkLOkO8pIUHh6uS5cuKSkpyW55lSpV7qsoAACQdZ0+Lb38stS7t9G1HgAAZK50BfmDBw+qX79++vPPP2W1Wu1+Z7FYFBUVlSHFAQCArGfUKCkgQJo1y+xKAADImdIV5AcMGKCyZctq9uzZ8vX1lcViyei6MlV8fLysVqtcXFzk9O/kt0lJSUpISJDFYpHrLRf+JSQkKCkpSc7OznJ2dr7ntlarVfHx8ZIkNze3B9LW1dXVtk8SExOVmJh4T22dnJzk4nLzpREXF/dA2qb2vN9L29s971mhrVn7/n5fJ5m17+/3deJo+z6rvU44Rpjf1lGPEYmJiZKkkyelb76RXF3jFBeX9V4njrbvs9rrhGOE+W0d9RjB/xEcI9LSNqceIzJaurZ45swZLVu2LNtMNbdkyRKdOXNG7du3V6VKlSRJ58+f16effipvb28NHjzY1nbFihU6duyYWrdubRvYLzw8XHPnzlW+fPn02muv2dquXr1av//+u1q2bKnatWtLkiIiIvThhx/K3d1dI0eOtLVdu3atDh06pGbNmql+/fqSpKioKE2fPl1OTk4aO3asre2GDRu0f/9+NWzYUI0aNZIkxcbGavLkyZKMWQWS30ibN2/Wrl27VK9ePT3577xASUlJevfddyVJI0aMUK5cuSRJP/30k7Zt26aaNWuqVatWtvubPHmykpKSNHToUHl6ekqSdu/erU2bNqlq1apq06aNre20adMUGxurQYMGycfHR5J04MABrV+/XoGBgerQoYOt7axZsxQVFaUBAwaocOHCkqTDhw/r66+/VtmyZdW1a1db2zlz5igiIkK9e/dWsWLFJElHjhzRypUrVbx4cfXq1cvWdv78+bp48aKef/5522v0+PHjWrZsmYoUKaJ+/frZ2i5evFjnzp1Tp06dVKFCBUnS2bNntWjRIhUqVEgDBw60tf3iiy908uRJtW3bVg8//LAkKTQ0VJ988om8vLz06quv2tquXLlSf/75p55++mk98sgjkqRLly5p9uzZypMnj4YNG2Zr+8033+jw4cNq3ry56tatK0m6evWqZs6cKVdXV40ePdrWdt26dTp48KAaN26sBg0aSJJiYmI0depUSdL48eNtbTdt2qQ9e/boscceU9OmTSUZB5PkfT9q1CjbQXvr1q3avn276tSpoxYtWti2kdw2KChIHh4ekqQdO3YoJCRE1atX17PPPmtrO3XqVMXHx+uVV15R/vz5JUn79u3Thg0bVKVKFbVr187WdubMmYqJidFLL70kX19fSdIvv/yitWvXqnz58urcubOt7UcffaSrV6+qb9++euihhyRJv/76q1avXq1SpUqpe/futrbz5s3TpUuX1LNnT5UoUUKSdPToUS1fvlwBAQHq06ePre3ChQt14cIFdenSReXKlZMknTp1Sp9//rn8/Pz04osv2tpyjOAYwTHCOEYUKFBZkjR0qFStmvR//8cxQuIYwTGCYwT/R3CM4Bhx92NEkSJFlJHSNY98o0aNdPjw4QwtBAAAZG27dxtfO3Uytw4AAHI6S3R0tPXuzexdvnxZ/fv3V82aNRUYGGjXfUCS3ScsWU1kZKT8/f119epV2yc+dHehuwtd4ugSl1FtOUZwjMiOx4i4uES1aJGov/8OV5s289W/f3/5+/tzjMigfZ/VXiccI8xv62jHCP6P4BiRFV8nWe0Yce3aNXl5eSk0NNSWQ+9HuoL8d999p759+6Y6qF1WH+wutSAPAABu7+23pfHjpW++CdWBA8G2IA8AANImMjIyQ4N8urrWBwUFqUuXLjpx4oSuXbtmd8vKIR4AANyb7dulN9+UxoyR/r1UFwAAmCxdQT4iIkKDBg2Sn59fRtcDAACyiIgIqWtX6dFHpXHjzK4GAAAkS1eQf/bZZ/Xjjz9mdC0AACCLsFqlvn2la9ekJUukBzBzDgAASKd0/VkuW7asxo8fr507d6pSpUopBru7daoNAADgeObMkVavllatkv6diQcAAGQR6QryCxculIeHh7Zv367t27fb/c5isRDkAQBwYIcPG3PFv/SS1Lat2dUAAID/SleQ//333zO6DgAAkAXExBjzxJcrJ73/vtnVAACA1HDFGwAAsHn1Ven0aWn/fil3brOrAQAAqUlXkB8xYkSqyy0Wi3LlyqVSpUrp6aeflre3930VBwAAMs+XX0rz5knBwVJgoNnVAACA20lXkP/f//6nX375RYmJiSpbtqysVqtOnDghZ2dnlStXTvPmzdPo0aO1ceNGVaxYMaNrBgAAGez0aalfP6lDB2O0egAAkHWla/q5Vq1aqXHjxjp+/Lh27NihnTt36tixY2rSpIk6dOigY8eOqX79+rc9cw8AALKO+Hhjvvj8+Y2z8RaL2RUBAIA7SVeQnzFjhsaOHStPT0/bMk9PT40ePVrTp09Xnjx5NHLkSP3yyy8ZVScAAHhA3nxT2rtXWrbMCPMAACBrS1eQj4yM1KVLl1Isv3z5sqKioiRJ+fPnV1xc3P1VBwAAHqgtW6R335XefluqV8/sagAAQFqku2v9Sy+9pG+++UZ//fWXLly4oG+++UYDBw7U008/LUnav3+/ypQpk6HFAgCAjHPpkvT881KTJhJXwwEA4DjSNdjdrFmzNGLECPXs2VMJCQnGhlxc1K1bN02ePFmSVK5cOX300UcZVykAAMgwSUlSr17G9fGffSY5peujfQAAYIZ0Bfm8efPqo48+0uTJk3Xq1ClZrVaVKlVKefPmtbWpWrVqhhUJAAAy1syZ0rp10nffSUWKmF0NAAC4F+kK8sny5s2rKlWqZFQtAAAgE+zfb3SlHzpUeuops6sBAAD3Ks1BvkuXLpo7d648PT3VpUuXO7ZdtmzZfRcGAAAy3j//SB07SlWrGoPcAQAAx5PmIO/p6SnLvxPL3jrtHAAAcAxWq9Snj/T339LmzZK7u9kVAQCA9EhzkJ87d67t+xkzZigpKUkeHh6SpDNnzujbb79V+fLl9cQTT9xTAcHBwZoxY4bCwsJUsWJFvffee6pfv/5d19u1a5eaN2+uwMBA7d69+57uEwCAnGjmTGn1auNWsqTZ1QAAgPRK1xi1HTt2tHWf/+eff9SoUSN98MEH6ty5s+bNm5fm7axcuVLDhw/X8OHDtXPnTj366KNq27atzp07d8f1rl69qn79+qlRo0bpKR8AgBxnzx5p2DDjuvg2bcyuBgAA3I90BflDhw7p0UcflSStWbNGvr6++uOPPzRv3jzNnj07zduZNWuWevbsqV69eqlChQqaMmWKihYtetcPA4YMGaKOHTuqTp066SkfAIAcJSLCuC6+Zk1p0iSzqwEAAPcrXUE+JiZG+fLlkyRt3rxZrVu3lpOTk2rXrq2zZ8+maRtxcXE6ePCgmjZtare8SZMm2rNnz23X++yzz3Ty5EmNHj06TfcTGxuryMhI2y0qKipN6wEAkB0kJUk9e0rXrknLl0tubmZXBAAA7le6gnypUqX07bff6vz589q0aZMtjF+6dMkW8O/mypUrSkxMlK+vr91yPz8/Xbx4MdV1jh8/rnHjxmnBggVycUnb5f1Tp06Vv7+/7VauXLk0rQcAQHbw/vvS2rXSZ59JxYqZXQ0AAMgI6Qryo0aN0ujRo1WxYkXVrFnT1sV906ZNqlq16j1tK3kk/GRWqzXFMklKTExU7969NWbMGJUtWzbN2w8KClJoaKjtdvTo0XuqDwAAR7VjhzRqlDR8uNSqldnVAACAjJLmUetv1bZtW9WrV09hYWF6+OGHbcsbN26sZ599Nk3b8PHxkbOzc4qz7+Hh4SnO0ktSVFSUfv75Zx06dEivvfaaJCkpKUlWq1Wenp765ptvUh38zt3dXe7MrwMAyGEuX5Y6dZLq1pXeecfsagAAQEZKV5CXpMKFC6tw4cJ2y2rWrJnm9d3c3FS9enVt2bLFLvyHhISoVSqnDTw9PbV37167ZfPmzdO2bdv0+eefq0SJEvf2AAAAyKaSkqTu3aXYWOmLLyRXV7MrAgAAGSndQT4jDB48WH379lX16tVVp04dLViwQOfOnVPfvn0lSePGjdOFCxf0ySefyMnJSZUqVbJbv1ChQnJ3d0+xHACAnGzyZGnDBmndOqloUbOrAQAAGc3UIN++fXtFRERo0qRJCgsLU2BgoFatWqVi/47GExYWpvPnz5tZIgAADuXHH6UxY6TRo6UWLcyuBgAAPAiW6Ohoq9lFZKbIyEj5+/vr6tWr8vT0NLscAAAyzF9/STVqSIGB0saNUhoneEmz0NBQBQcHq3///vL398/YjQMAkI1FRkbKy8tLoaGhGZJD0zVqPQAAyFpiY6XnnjPmiV++PONDPAAAyDr4Mw8AQDYwZIh08KD0009SKpO/AACAbIQgDwCAg/vkEyk42Phau7bZ1QAAgAeNrvUAADiwvXull1+WBgyQXnjB7GoAAEBmIMgDAOCgwsON6+Jr1JBmzjS7GgAAkFkI8gAAOKD4eKljR+PrypWSu7vZFQEAgMzCNfIAADig4cOlHTukLVukhx4yuxoAAJCZCPIAADiYpUulGTOkDz6QHn/c7GoAAEBmo2s9AAAO5JdfpL59pe7dpUGDzK4GAACYgSAPAICDiIiQ2rWTKlSQ5s6VLBazKwIAAGagaz0AAA4gIUHq0kWKjDSui8+d2+yKAACAWQjyAAA4gKAgafNm6fvvpRIlzK4GAACYiSAPAEAWN2+eMU/8hx9KzZqZXQ0AADAb18gDAJCFbdsmDRwovfSS9PLLZlcDAACyAoI8AABZ1MmT0nPPSQ0bGmfkAQAAJII8AABZUmSk9MwzUoEC0ooVkqur2RUBAICsgmvkAQDIYuLjpY4dpb/+knbvlry9za4IAABkJQR5AACyEKtVGjTo5gj1FSqYXREAAMhqCPIAAGQhU6ZIwcHSggVS06ZmVwMAALIirpEHACCL+PJLacQI6Y03pN69za4GAABkVQR5AACygJ07pe7dpa5dpbffNrsaAACQlRHkAQAw2bFjUuvWUu3aRpd6i8XsigAAQFZGkAcAwERhYVLz5pKPj7R6teTubnZFAAAgq2OwOwAATBIZKbVsKcXGSiEhRpgHAAC4G4I8AAAmiI2V2raVTp2SfvpJKl7c7IoAAICjIMgDAJDJkpKkHj2kHTukDRukKlXMrggAADgSgjwAAJnIapWGDjWmmvvyS6lhQ7MrAgAAjoYgDwBAJnrzTemDD6SPP5aee87sagAAgCNi1HoAADLJ++9Lb70lTZokvfSS2dUAAABHRZAHACATzJsnBQVJo0dLI0aYXQ0AAHBkBHkAAB6wL76QBgyQBg2S3nnH7GoAAICjI8gDAPAAffut1L27cZs5U7JYzK4IAAA4OoI8AAAPyNq1xoB2rVtL8+dLTvzVBQAAGYB/KQAAeADWrTNC/NNPS8uWSS7MEwMAADIIQR4AgAz2/fdS27bSU08Z18e7uppdEQAAyE4I8gAAZKANG6Q2baQWLaTlyyU3N7MrAgAA2Q1BHgCADLJunXE9/BNPSCtWEOIBAMCDQZAHACADrFx580z8ypWSu7vZFQEAgOyKIA8AwH367DOpUyepfXvpyy8J8QAA4MEiyAMAcB/mzJF69pR695YWL2ZgOwAA8OCZHuSDg4MVGBgob29v1a9fXzt27Lht26+//lpPP/20ihcvrsKFC6tx48bauHFjJlYLAMBN778vvfSSNGSIFBwsOTubXREAAMgJTA3yK1eu1PDhwzV8+HDt3LlTjz76qNq2batz586l2n779u1q0qSJVq1ape3bt6tBgwbq0KGDfvnll8wtHACQoyUlScOGSUFB0ujR0owZkpPpH40DAICcwhIdHW01684bNmyoatWqaebMmbZlNWrU0NNPP6233norTduoWbOmnnvuOY0aNSpN7SMjI+Xv76+rV6/K09MzXXUDAHKu+HipTx9pyRIjwA8ZYnZFmSc0NFTBwcHq37+//P39zS4HAACHERkZKS8vL4WGhmZIDjXt/EFcXJwOHjyopk2b2i1v0qSJ9uzZk6ZtJCUlKSoqSgUKFHgQJQIAYOfaNemZZ4z54Zcty1khHgAAZB0uZt3xlStXlJiYKF9fX7vlfn5+2rRpU5q2MXPmTMXExKhdu3a3bRMbG6vY2Fjbz1FRUekrGACQo126JLVqJf3xh7R+vfSfz6EBAAAyjWlBPpnFYrH72Wq1pliWmhUrVmjixIlavnx5ig8DbjV16lRNnDjxvusEAORcv/8uPf20FBMjbdsmVa9udkUAACAnM61rvY+Pj5ydnXXx4kW75eHh4XcM5pIxSN7AgQO1ePFiNWnS5I5tg4KCFBoaarsdPXr0vmsHAOQcGzdK9epJHh7Snj2EeAAAYD7Tgrybm5uqV6+uLVu22C0PCQlRnTp1brveihUrNGDAAH366adq0aLFXe/H3d1dnp6etlu+fPnuu3YAQM4wZ47UsqVUv760Y4dUvLjZFQEAAJjctX7w4MHq27evqlevrjp16mjBggU6d+6c+vbtK0kaN26cLly4oE8++USSEeL79eunKVOmqFatWgoLC5Mk5c6dW15eXqY9DgBA9pKQIA0fLk2fLg0aZHx1Mf1iNAAAAIOp/5a0b99eERERmjRpksLCwhQYGKhVq1apWLFikqSwsDCdP3/e1n7BggVKSEjQ0KFDNXToUNvybt26KTg4ONPrBwBkP1euSJ07SyEh0gcfSIMHm10RAACAPdPPL/Tv31/9+/dP9Xf/Defff/99ZpQEAMihfvlFatvWmGbuhx+kuwzDAgAAYArTrpEHACArWbpUevRRydtb2r+fEA8AALIugjwAIEeLi5OGDpW6dZM6dJC2b2dQOwAAkLWZ3rUeAACznDoldepkdKn/4ANjYDuLxeyqAAAA7owgDwDIkVatkvr0MbrS79gh1apldkUAAABpQ9d6AECOEhsrDRkiPfec1KyZ9PPPhHgAAOBYOCMPAMgx/vc/6fnnpT//lD78UBo4kK70AADA8XBGHgCQ7SUmSlOn3jzzvm+f9PLLhHgAAOCYCPIAgGztzBmpaVNp+HCjS/3evdLDD5tdFQAAQPrRtR4AkC0lJUnBwUaAL1BA2rJFatTI7KoAAADuH2fkAQDZzrFjUuPG0ksvSZ07G9fGE+IBAEB2QZAHAGQbCQnSe+8ZXefPn5c2bzbOynt5mV0ZAABAxiHIAwCyhZ07jcHsRo0yBrI7fFhq0sTsqgAAADIeQR4A4NDCw6U+faT69SVnZ2n3bmOE+jx5zK4MAADgwWCwOwCAQ0pMNLrNjx5tTCM3e7bUr58R5gEAALIzzsgDABzOhg1StWrSwIHSc89JR49KL75IiAcAADkDQR4A4DAOH5ZatDBuBQoYc8J/8olUsKDZlQEAAGQegjwAIMs7d87oNl+tmnTihLRqlbRtmzG4HQAAQE7DNfIAgCwrLEyaOFGaO1fy9JSmTTPmhndzM7syAAAA8xDkAQBZzuXL0pQp0qxZkru7NH68NHiwlC+f2ZUBAACYjyAPAMgy/vpLev994wy8k5MUFCS99pqUP7/ZlQEAAGQdBHkAgOmOH5cmT5YWLZI8PKTXX5eGDGEQOwAAgNQQ5AEAprBape3bpRkzpDVrpEKFpHfeMaaR8/Q0uzoAAICsiyAPAMhUcXHS8uVGgP/5Z6lCBemjj6SePaXcuc2uDgAAIOsjyAMAMsXp09K8edL8+dLFi1Lz5tL69dKTTxrXwwMAACBtCPIAgAcmIUH67jtj8LrvvzdGne/eXRo4UAoMNLs6AAAAx0SQBwBkuMOHjYHrliwx5oKvVcs4G9+5szGYHQAAANKPIA8AyBChodKKFUaAP3hQ8vGRunaVevWSatQwuzoAAIDsgyAPAEi3S5ekr74yBq/btk1ycZGefloaP15q2VJyczO7QgAAgOyHIA8AuCfnz0tff21MGRcSYixr2lT65BOpbVupQAFTywMAAMj2CPIAgDuyWqX//U9au9YI7/v3G2feGzc2po1r186YAx4AAACZgyAPAEjh6lVp0yZp3TpjtPkLF6S8eY3u8kOHSk89JeXPb3aVAAAAORNBHgCgyEhpxw5p61bjduCAlJgoVaxojDTfsqX0+OOSu7vZlQIAAIAgDwA5UGSktH27fXBPSpL8/Y0u8y+8IDVvLhUvbnalAAAA+C+CPABkc0lJ0rFj0r59xm3XrpvBvUgRqVEjqV8/42uZMpLFYnbFAAAAuBOCPABkI1ar9Ndf0t69N4P7/v3GNe+SEdTr1CG4AwAAODKCPAA4qNhY6Y8/pMOHpV9/Nb7+/LMUFmb83t9fql1bGjZMqlVLqllT8vY2t2YAAADcP4I8AGRxcXHSqVPSb7/dDOy//mp0l09MNNoUKyZVriz17m2E91q1pIceMrduAAAAPBgEeQDIAuLjjbB+7Jh0/Lj91zNnbgb2ggWlKlWkJ54wpoGrXFmqVEny8jK3fgAAAGQegjwAZIIbN6Rz54xQfvbszduZM9Lp0/ZhPVcuqXRpqWxZqV0742vZslJgoOTryzXtAAAAOR1BHgDuQ2KiFB4uhYamfvvrLyOkh4fbr+fvb0ztVqyYVKPGzbBepozRJd7JyZzHAwAAgKyPIA8At4iLk/75R7p8Wbp06ebXW79P/hoWZgT0pKSb61ssUqFCRlD395ceflh65hkjsBcrZoT3hx6S3N1Ne4gAAABwcKYH+eDgYM2YMUNhYWGqWLGi3nvvPdWvX/+27X/66SeNHDlSR44ckb+/v4YOHaq+fftmYsUAsqrERCk6Wrp2zbhFRRnTrv39txHOb739d1nyzzExKbfr7Cz5+BgBvVAh4zr10qWlwoVvBvbkm5+f5GL6kRUAAADZman/bq5cuVLDhw/XjBkzVLduXc2fP19t27bVgQMHFBAQkKL96dOn1a5dO/Xq1Uvz58/X7t279eqrr6pgwYJq06ZN5j8AAGmSlGRMlXb9unGt+PXr9t/f7ev16/YB/dagfuvP16/fuQ5PTyl/fvtb6dJSgQIplycH9kKFjJ/p6g4AAICswtQgP2vWLPXs2VO9evWSJE2ZMkWbN2/WvHnz9NZbb6Vo/8knnyggIEBTpkyRJFWoUEE///yzZs6cSZBHlme13rwlJd38mpiY+i0h4fa/y8h14uON7uQP4uuNG8YtNvbenisnJyl3bmPQt+Sv+fJJefMaNy8vo3t68s93uiUHc09PzpQDAAAgezDt39q4uDgdPHhQr7/+ut3yJk2aaM+ePamus3fvXjVp0sRuWbNmzbRo0SLFx8fL1dU1xTqxsbGKvSVFREVFSZJefDFMbm7Rdm2tVt325zv97r9ut969bD89dWXENu60HTOfn7tt42635GuYbw3R0s3v77d9WtbNipydJVdXI+Am35J/vt3XXLmMgHy39VxcjOvA3dyMr7e7ubkZ20xulyuXUVdGjsweG2tc0w7g/ly+fNnuKwAASJvkHJpRTAvyV65cUWJionx9fe2W+/n5adOmTamuc/HiRfn5+dkt8/X1VUJCgi5fvix/f/8U60ydOlUTJ05Msbx48U+VK1eu+3gEAO7Ear15Rh5A9rJq1SqzSwAAwKHcyOB/ik3vaGr5z2k3q9WaYtmdWP893Xm7dYKCgjR48GDbz1FRUSpXrpx69+6tfPnypaNiAABypsuXL2vVqlVq166dChYsaHY5AAA4jKioKE2aNCnDtmdakPfx8ZGzs7MuXrxotzw8PDzFWfpkfn5+KdpfunRJLi4u8vHxSXUdd3d3uacyz1PhwoXl6emZzuoBAMi5ChYsmGovOAAAkDoPD48M3Z5p4zC7ubmpevXq2rJli93ykJAQ1alTJ9V1ateurZCQELtlmzdvVo0aNVK9Ph4AAAAAgOzG1AmVBg8erIULF2rRokX6448/NHz4cJ07d842L/y4cePs5ojv27evzp49qxEjRuiPP/7QokWLtGjRIr3yyitmPQQAAAAAADKVqdfIt2/fXhEREZo0aZLCwsIUGBioVatWqVixYpKksLAwnT9/3ta+RIkSWrVqlUaMGKHg4GD5+/tr6tSpTD0HAAAAAMgxLNHR0Vl4cqyMFxkZKX9/f129epVr5AEAuAehoaEKDg5W//79uUYeAIB7EBkZKS8vL4WGhmZIDjW1az0AAAAAALg3BHkAAAAAABwIQR4AAAAAAAdCkAcAAAAAwIEQ5AEAAAAAcCAEeQAAAAAAHAhBHgAAAAAAB0KQBwAAAADAgRDkAQAAAABwIAR5AAAAAAAcCEEeAAAAAAAHQpAHAAAAAMCBEOQBAAAAAHAgBHkAAAAAABwIQR4AAAAAAAdCkAcAAAAAwIEQ5AEAAAAAcCAEeQAAAAAAHIiL2QVkNqvVKkmKjIw0uRIAABxLVFSUbty4oaioKHl4eJhdDgAADiM5fybn0ftliY6OzpgtOYiTJ0+qSpUqZpcBAAAAAMhhDh8+rFKlSt33dnLcGXlvb29J0p9//ilPT0+TqwHwX1FRUSpXrpyOHj2qfPnymV0OgFvw/gSyNt6jQNYVGRmp8uXL2/Lo/cpxQd7JyRgWwNPTkyAPZGH58uXjPQpkUbw/gayN9yiQdSXn0fveToZsBQAAAAAAZAqCPAAAAAAADiTHBXl3d3eNHj1a7u7uZpcCIBW8R4Gsi/cnkLXxHgWyrox+f+a4UesBAAAAAHBkOe6MPAAAAAAAjowgDwAAAACAAyHIAwAAAADgQAjyAAAAAAA4kBwV5N977z01adJEBQsWVJEiRVJtc+7cObVv316FChVSsWLFFBQUpLi4uEyuFIAkVaxYUR4eHna3sWPHml0WkGMFBwcrMDBQ3t7eql+/vnbs2GF2SQAkTZgwIcXfy5IlS5pdFpAjbd++Xe3bt1fp0qXl4eGhb7/91u73VqtVEyZMUOnSpeXj46MWLVro999/v+f7yVFBPi4uTm3btlXfvn1T/X1iYqLatWun6Ohobdy4UQsXLtSaNWs0atSoTK4UQLKxY8fqxIkTttuIESPMLgnIkVauXKnhw4dr+PDh2rlzpx599FG1bdtW586dM7s0ADI+/L717+XevXvNLgnIkaKjo1WlShVNmzYt1d9PmzZNs2bN0rRp0/Tjjz/Kz89PzzzzjKKiou7pflwyolhHMWbMGEnS4sWLU/39pk2b9Mcff+jo0aPy9/eXJL377rsaMGCAxo8fL09Pz0yrFYAhb968Kly4sNllADnerFmz1LNnT/Xq1UuSNGXKFG3evFnz5s3TW2+9ZW5xAOTi4sLfSyALaN68uZo3b57q76xWqz766CMNGzZMrVu3lmT0ditZsqRWrFihF154Ic33k6POyN/N3r17FRgYaAvxktSsWTPFxsbq4MGDJlYG5FzTpk1TQECA6tatq/fee49LXQATxMXF6eDBg2ratKnd8iZNmmjPnj0mVQXgVidOnFDp0qUVGBionj176tSpU2aXBOA/Tp8+rYsXL9r9PXV3d9djjz2m3bt339O2ctQZ+bu5ePGifH197ZYVKFBAbm5uunjxoklVATnXwIEDVa1aNeXPn18HDhzQ+PHjdfr0aX388cdmlwbkKFeuXFFiYmKKv5F+fn7atGmTSVUBSFazZk3NmzdPZcqUUXh4uG1cqP3798vHx8fs8gD8KzlT+vn52S339fXV2bNn72lbDh/kJ0yYoIkTJ96xzU8//aQaNWqkaXsWiyXFMqvVmupyAPfuXt6zgwcPti2rUqWK8ufPr27duuntt9/mHxPABP/9W8jfRyBr+G833jp16qhy5cpasmSJhgwZYlJVANIqPX9PHT7IDxgwQO3bt79jm+LFi6dpW35+ftq3b5/dsr///lvx8fEpzkIASJ/7ec/Wrl1bknTy5EmCPJCJfHx85OzsnKJ3Wnh4OH8fgSzIw8NDlSpV0okTJ8wuBcAtks/EX7x40e5y7kuXLt3z31OHD/IFCxZUwYIFM2RbtWvX1nvvvafQ0FDbE7t582a5u7urevXqGXIfQE53P+/ZQ4cOSRKD+QCZzM3NTdWrV9eWLVv07LPP2paHhISoVatWJlYGIDWxsbH6888/Vb9+fbNLAXCLEiVKyM/PT1u2bFG1atUkGePQbN++XW+//fY9bcvhg/y9OHfunCIiInT+/HklJibaQkHp0qWVN29eNWvWTBUqVFDfvn01YcIE/f333xo9erR69+7NiPVAJtuzZ4/27t2rBg0ayMvLSwcOHNCIESPUqlUrBQQEmF0ekOMMHjxYffv2VfXq1VWnTh0tWLBA586du+2UrgAyz6hRo/TUU08pICBAly5d0uTJkxUVFaVu3bqZXRqQ41y7ds2uN8zp06d16NAheXt7KyAgQC+//LKmTp2qMmXKqHTp0poyZYpy586tjh073tP9WKKjo60ZXXxW1b9/fy1ZsiTF8vXr16tBgwaSjLD/6quvatu2bbYndOLEiXJ3d8/scoEc7eDBgxo6dKiOHj2q2NhYFStWTO3bt9fQoUOVJ08es8sDcqTg4GBNnz5dYWFhCgwM1OTJk/XYY4+ZXRaQ4/Xs2VPbt2/XlStXVLBgQdWuXVtjx45VxYoVzS4NyHF+/PFHtWzZMsXybt26KTg4WFarVRMnTtT8+fP1zz//qFatWpo2bZoqVap0T/eTo4I8AAAAAACOjnnkAQAAAABwIAR5AAAAAAAcCEEeAAAAAAAHQpAHAAAAAMCBEOQBAAAAAHAgBHkAAAAAABwIQR4AAAAAAAdCkAcAAAAAwIEQ5AEAQJq0aNFCw4YNM7sMAAByPII8AAAAAAAOxBIdHW01uwgAAJC19e/fX0uWLLFb9vvvv6t48eImVQQAQM5FkAcAAHd19epVtW3bVoGBgRozZowkqVChQnJ2dja5MgAAch4XswsAAABZn5eXl9zc3JQ7d24VLlzY7HIAAMjRuEYeAAAAAAAHQpAHAAAAAMCBEOQBAECauLq6KikpyewyAADI8QjyAAAgTYoXL659+/bpzJkzunz5MqEeAACTEOQBAECavPLKK3J2dtYjjzyi4sWL69y5c2aXBABAjsT0cwAAAAAAOBDOyAMAAAAA4EAI8gAAAAAAOBCCPAAAAAAADoQgDwAAAACAAyHIAwAAAADgQAjyAAAAAAA4EII8AAAAAAAOhCAPAAAAAIADIcgDAAAAAOBACPIAAAAAADgQgjwAAAAAAA6EIA8AAAAAgAP5f/OhTkALG1UDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "sigma_x = np.arange(-10,10,0.1)\n",
    "sigma_y = 1 /(1 + np.power(np.e, -sigma_x))\n",
    "fig, ax = plt.subplots(1,1,figsize=(12,4),facecolor='whitesmoke', edgecolor='gray')\n",
    "ax.plot(sigma_x, sigma_y, lw=1, ls= '-', color='blue',label=\"sigmoid core function\")\n",
    "fig.suptitle(\"function show\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_xlabel(\"t\")\n",
    "ax.set_ylabel(\"sigmoid\")\n",
    "ax.set_xticks(np.arange(-10,10.1,5))\n",
    "ax.set_yticks(np.arange(0,1.2,0.2))\n",
    "ax.set_xlim(-10,10)\n",
    "ax.set_ylim(-0.1,1.1)\n",
    "ax.set_title('sigmoid function show')\n",
    "ax.axhline(0, color='grey', linewidth=1)\n",
    "ax.axvline(0, color='grey', linewidth=1)\n",
    "ax.hlines(0.5,-12,12, ls=':', color='gray')\n",
    "ax.hlines(1.0,-12,12, ls=':', color='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "36ff43e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{1}{1 + e^{- t}}$"
      ],
      "text/plain": [
       "   1   \n",
       "───────\n",
       "     -t\n",
       "1 + ℯ  "
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "init_printing(use_unicode=True)\n",
    "\n",
    "t = symbols(\"t\")\n",
    "ft = 1/(1 + exp(-t))\n",
    "ft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b83ca50d",
   "metadata": {},
   "source": [
    "## attribute of sigmoid function\n",
    "1. derivitives\n",
    "$$\n",
    "    \\sigma^{\\prime}(x) = \\sigma(x) \\cdot (1-\\sigma(x))\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "174fd098",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{e^{- t}}{\\left(1 + e^{- t}\\right)^{2}}$"
      ],
      "text/plain": [
       "    -t    \n",
       "   ℯ      \n",
       "──────────\n",
       "         2\n",
       "⎛     -t⎞ \n",
       "⎝1 + ℯ  ⎠ "
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ft = diff(ft, t)\n",
    "df_ft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39ba8b03",
   "metadata": {},
   "source": [
    "## decision boundary\n",
    "1. take place where $\\sigma(\\theta \\cdot x) = 0.5$ . This time entries has equal probabiliy to be classified in either class\n",
    "2. for linear model in sklearn <font color=maroon><b>(LogisticRegression)</b></font>, <font color=maroon><b>predict()</b></font> will output its final class while <font color=maroon><b>predict_proba()</b></font> will output its original decision value, a number between 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "61d010d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename', 'data_module'])\n",
      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
      "['setosa' 'versicolor' 'virginica']\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "raw_iris = load_iris()\n",
    "print(raw_iris.keys())\n",
    "print(raw_iris[\"feature_names\"])\n",
    "print(raw_iris[\"target_names\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "01a79774",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select oetal length feature\n",
    "X_iris = raw_iris.data[:,3].reshape(-1,1)\n",
    "# select virginica as target, make a binary classifier\n",
    "y_iris = (raw_iris[\"target\"] == 2).astype(np.int64)\n",
    "# initiate classifier\n",
    "logis_reg = LogisticRegression()\n",
    "logis_reg.fit(X_iris, y_iris)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "c958c8bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA+kAAAEmCAYAAAAeHNE3AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAA9hAAAPYQGoP6dpAACMFklEQVR4nOzdd3QU5dvG8e+mh4QEEkih19CRIk2qiIaiSEdFBQHBnwiioggoKvKKBQHFCtLEAkhTBBXpHaRKB+klCU3SgLSd948xm4QkkISQTbk+58zZ2ZlnZu4NyyT3PM0SHR1tICIiIiIiIiJ252DvAERERERERETEpCRdREREREREJJdQki4iIiIiIiKSSyhJFxEREREREckllKSLiIiIiIiI5BJK0kVERERERERyCSXpIiIiIiIiIrmEknQRERERERGRXMLJ3gHkNKvVSkhICJ6enlgsFnuHIyIiIiIiIvmcYRhERUURGBiIg8Ot68oLXJIeEhJCUFCQvcMQERERERGRAubIkSOULFnylmUKXJLu6ekJwJkzZ/Dy8rJzNCIiIiIiIpLfRUREULp0aVs+eisFLklPbOLu5eWlJF1ERERERERyTEa6XGvgOBEREREREZFcQkm6iIiIiIiISC6hJF1EREREREQkl7Brkr5hwwa6detGxYoV8fDwYMmSJbc9Zv369TRt2hQfHx9q1KjBN998kwORioiIiIiIiNx9dk3So6OjqVWrFhMmTMhQ+ZMnT9KlSxfuu+8+Nm3axKuvvsqwYcNYvHjx3Q1UREREREREJAfYdXT34OBggoODM1z+m2++oXTp0nz00UcAVK1alZ07d/LJJ5/QqVOnuxSliIiIiIiISM7IU1Owbdu2jdatW6fY1qZNG2bNmkVcXBzOzs6pjomJiSEmJsb2PjIy8q7HmV22boUJE8BiSXvp3x9atjTL7t0LEyemX7ZnT7j/frPsP//Ap5+mX7Z9e0j8MZ87B59/nn7Zli2Tznv5Mnz1VfplGzSAVq3MspGRMH16+mVr1IAWLcyyMTHw44/g4GAujo4p18uUgXvvNctarbBiRfplfX2hcuWkn/G+fUn7by5fqBAUL55U9soVM7b0zu3oeFe+BiIiIiIi+ZZhGCQYCSRYE1K8Wg1rqm3JX62GNcW2asWq4e7sbu+Pky3yVJIeFhaGv79/im1+fn7Ex8dz6dIlAgMDUx0zfvx43nvvvZwKMVudOQPz5qW///77k5L0s2dhxoz0y9aokZRMnzsHkyenX7Z48aQkPSQExo1Lv+ybbyad98IFeOON9Mu+/HJSkn7lCgwdmn7Z555LStIjI+GZZ9Iv+9RT8O235npMDNyqcUaXLrBgQdL72rXBMNIuGxwMv/+e9L5sWYiKSrtss2awfn3S+6AguHQJnJxSL7VqpYyhRw8IC0u7bOnSMGlSUtl334XQ0KT9zs7mq4sL+PjACy8klf3tN7h61dzn6mq+Ji6FCkGdOkllL182H3Ak7nd1NR8+iIjkZVarlZCQEAACAwNx0I1NRPIBq2ElNiE2xRITH5PyfUJMpvbHJcQRb40nzmq+3rykuz0h6+UTE2yDdP4Yz6R9/9tHDb8a2XIue8tTSXpajP8yrPQmhR82bBiDBw+2vY+MjCQoKChHYrtTdeqYNd6GkfbSsGFS2aAgeO+99Ms2apRUtkwZGDUqY2X9/ODFFzMWg7c39OuXftnE2m4wk8THHku/bN26SWWdnMzafasVEhLM1+TrN/9z1qmTftmAgKRyhmE+kEivrItLyvNaren/Wznd9D/p33/NJS1FiqR8v20bnDqVdtlq1VK+nzMHDhxIu2yZMimT9Lfegr/+Srusr6/5ECFR9+6wenXKMo6O5s+gcGHzIUKioUPNVh5ubuDunnJxc4NPPklK8P/4w/xsaZVzdzcfkiS2QDAMs6WCiEh2cXBwoGTJkvYOQ0TyMath5VrcNaJjo4mKjSI6zny9Hned6/HXuR53nRvxN1Kt34i/YSuT7rabyicm1PHWeHt/7BxlwYKjgyOOFscUrw4WhxTbHCz550FsnkrS/f39CUueLQAXL17EyckJX1/fNI9xdXXF1dU1J8LLdpUqQbLnC7dUsSKMGJGxsuXLw9ixGStbpkzKmtxbKVECMjrYfvHiZhP2jChSBJYuzVhZd3fYtStjZS2WlMnn7UREpE7kE9dvrpzZtg1iYyE+PvXiflMrnK++Mmvo0yrr7Z2y7KBBZszJy8TFmcvNyX+DBmaCHRubtMTEmK83l01ISP15ExLg+vXUDyAOHIAtW9L+GTk4mA+WEn39NSxalHZZgGvXkn4ezzwDc+eCp6e5eHgkrXt6wqxZST+PZctg//6U+728zP3e3uZ3/Oa4RURERBKsCUTGRhJ+I5yImAjCY8IJvxFue42MjUyVcCe+RsVGpdp3Le6avT8STg5OuDi6pFhcHV1Tb3NKY5ujK84Ozrg4uuDk4GRbnB2dU753SPk+rTKZKefk4JQq6U4vCU+vMjY/y1N/xjZs2JDffvstxbaVK1dSr169NPuji2SnzPQ7L18+4+dt2zbjZZ9/PuNlP/8842XXrjUfOMTFJSXyiUl9/E0Pa//v/8yHBdevm8uNG0nr8fEpa8MbNjST/eRlkh+X/PlZVJS57caNlLX8iZL/7OfPv3X3jjNnoFQpc33MGPOBkLe3+XAiMZFPXP/f/8yuAgDnz0N0NBQrZu5Ty1iRvM1qtbJv3z4AatasqebuIvmAYRhci7vG5euXuXL9Cpev/ff63/t/r/9LeEzaCXhETASRsXdvfCoPZw88XTzxcPGgkHMh3J3ccXNyw93ZPcW6m2PqbSn2O7nh7uSeYt3VyRVXR9dUibazgzOODhoYKb+xa5IeFRXFsWPHbO9PnjzJnj178PHxoXTp0owePZrz58/b5kLv378/X3/9NcOHD+eZZ55h69atzJo1i5kzZ9rpE4jkHw4OZtJ8u4YnDRpk/Jyvv57xstOmwccfm8l6dLT5mnwpVCipbNOmZvKfuC8y0mzpEB5u9sNP3gLh1Ck4dCj96/bpk7T+8cfmYI1g/jx8fMyuAb6+ZuL+2WfmOAEAe/bA8ePm9oAA8Pc3Wy4UwIe9IrlWfHw8i/5rzlO1alVcbu7HJCJ2FxMfw4XoC4RFh5mvUebr5euXzQT8xpVUyXhsQuwdX9fV0RUvVy+83bzxdvXG280bL1cvvFy98HQ2E21PF88Uibeni2ea2zycPXB3ds9Xza3FvuyapO/cuZN27drZ3r/+31/0vXr1YsqUKYSGhnL27Fnb/nLlyrFw4UKGDx/OlClTCAwMZPz48Zp+TSQfSKzhzoh+/cwlI0aNMgcXDA9PSuKTrxctmrK8p6eZ+FutZo1+8lr95K0Tvv02KaFP5O6elLB//z1UqGBu370bTpxI2hcQkPKhg4jcHRaLhQr//UcsiM0lRewl3hpPWFQY5yLPcT7yPCGRISkT8WQJeXhMeJau4ezgjG8hX3zdffFx98G3kC8+bj4UdS+aIulOXPd29U6RlLs65c3usFIwWKKjo7NnOL08IiIigsDAQMLDw/Hy8rJ3OCKSC8XEmCPeJ18uXTJr3RNbGkycaM6+cPGiOU7AzSP/nztnjtMA5swGEyem3O/tbdbKlypljktQtqy5/fRpsyVBqVJmzbyIiEhuEhUbxZnwM5yLPMe5iHO2RDz5+9CoUKzGLUbcvYmTgxN+Hn74e/jj7+mPn4cfxdyLJSXf7j4pk3F3HzycPfTwTfKUiIgIvL29CQkJuW0emqf6pIuI5ARXVzPBTkyy0/LSS+aSKDraTNZDQ81XP7+kfaVKQePG5r7QULPffWJt/r59KbsYTJqUlNB7eSUl8mXLmjXz/fubze9FRETuhvAb4ZwKP8XJqyc5efUkp66e4mT4f69XT3L5+uUMncfR4kiAZwAlvUoS6BmIv4eZfPt7+qdY9/Pwo6hbUSXcIskoSRcRyQYeHmYSndjEPbmXXzYXMKeai4gwB6k7c8Zckif0Fos5qN3Vq2a5/fvNJdHTTyetv/22OXp++fJJS4UKULmy+arxNEVE5GaGYXA+8jxHrxzlnyv/cPTyUY5eOcrxf49zKvwUV29cve05vFy9KFm4JCW9Spqvydf/e/Xz8NOAZiJZpCRdRCQHWSxJ/e+rVUu9/+OPkwbQO3vWXM6cMfu0nz5t9mdPtHcv/P23udzM0dEsn9ga4K+/zNr+oCAIDNQAd1IwxMXFMXXqVACeffZZzQQjBcqV61c4cPEAhy8d5uiVo7ak/J8r/9x22jBfd1/KFSlHuSLlKOtd1nwtUtb23tstg4PIiEiWKEkXEcmFPD2halVzSc/48Wbz9+PHzST+xAlz/ehRc+C75An9hx+aU9clnjsoCKpXh5o1oVYtePBB1bxL/mMYBhcvXrSti+RHF6MvcuDiAQ5cPMD+i/tt62HRYeke42hxpFyRclT2rUylopWo7FuZikUr2pJxTxfPHPwEInIzJekiInlUYhP3mxmGOaBd8imhAwKgYkUzkY+Kgp07zQXAxcWsZU80Y4b5PjGBVx94yaucnJzo3bu3bV0kL7sed519F/axO3Q3u0N3s//ifvZf3M+la5fSPaasd1mqFKtCZZ/K5uJrvpYrUg5nRz2ZFcmt9BtLRCSfsVhS9nMHmDzZfI2NhWPHzLnjDxwwB66Li4Pk+cvkybBrV9L7EiWgfn2oVw/uvRcefvjufwaR7ODg4EC5cuXsHYZIpl26dsmWjO8O3c2u0F0cunQozRHTLVgoX7Q81YtXp3qx6lQvXp0afjWoWqyqasRF8ihNwSYiIimMGQM7dph93k+cSLmvcmU4ciTp/dSpUKyYmcSXLq2+7iKS0u7Q3dyIv0Gjko00enc6ImIi2H5+O9vObWPrua38de4vzkWeS7Ns8ULFqRtYl3v876G2f22qF69O1WJVKeRcKIejFpHM0hRsIiKSZaNHJ61HRcGePWbT+B07UvZzt1rhlVcgMtJ8X6IENGliLvfdZ9a8J59eTiSnWa1Wjvz3VCkoKAiH5H1AJEf0/6U/O0J2UNOvJi82epEnaj1RoBPKuIQ49l3YZ0vIt53bxoGLBzBIXWdWyacSdQLqUDegLnUC6lAnoA6BnoF62CFSAKgmXUREsiQy0pwrPrHWPSEh5f62beG335Leh4SYI8uL5JTY2FjGjRsHwIgRI3BxcbFzRAVP7S9rs/fCXixYMDAo7FKYvnX7MqjBICr7VrZ3eHddZEwkm89uZt2pdaw/vZ6/zv3F9fjrqcqV9S5Lw5INaVSyEQ1KNqBuQF0Kuxa2Q8QicreoJl1ERO66woXhm2/M9WvXYPt22Lw5aWnYMKnshQtmTXuFCtCqVdJSurQdApcCw2KxUPq/L5lqH+0rsaY4MjaSz7Z9xidbP+GB8g8wpNEQOlTukG/m074YfZENpzfYkvJdobtS9SP3dvWmYcmGtqS8YcmG+Hv62yliEcmNVJMuIiLZzjDMQeoSm7uvWgUPPZS6tj0xae/Xz2wiL5LdToef5vi/x+0dRoHV9+e+nLh6Is19jhZHEowEShQuwQsNXqBfvX74efilWTa3Cr8RzpqTa1hxfAUrT6zk4KWDqcqUL1Ke5mWb07xMc5qVaUaQbxAOFnW9ECloMlOTriRdRERyRGQkbNwIa9aYy/btSUn7zJnw30xZnDkDu3fD/febc7qL3Inqn1dPM3GS3MXB4oCDxYEe1XvwQsMXaFyqca5s/RCbEMuWs1tYcXwFK46vYNu5bSQYKZ8+1vSrSfMyZlLevGxzSnmVslO0IpKbqLm7iIjkOoULm/3U27Y130dEJCXtrVsnlfvpJ3NAOmdnaNrULB8cDPfco9HjJfOiYqPsHYJkgNWwYjWszDswjx/2/UAtv1oMaTQkVww0d+zKMZYeXcofx/5g7cm1RMdFp9hf2acyD1Z4kAcqPEDLsi3xLeRrp0hFJL9QTbqIiOQqn38OH3+cevo3f38zWR83zuzfLnI7cXFx+L/vz7/Wf+0dimRS8oHm+tfrz3sPvIebk1uOXDsuIY6NZzay9MhSfj36K4cuHUqxv3ih4rSp0IY2FdrwQPkHKFukbI7EJSJ5m5q734KSdBGR3M8w4J9/4I8/zGX1aoiOBjc3uHQJPDzMcn/9BSVLKmmXtMXGxlJ8XHEiiLB3KHIHPF082fe/fXc1Gf73+r/8euRXfj36K3/88wfhMeG2fU4OTjQr04z2ldrzUMWHqOVfS33KRSTT1NxdRETyNIsFKlc2lxdegJgYs2n8iRNJCTpA//7w999w773w6KPmUrOmmsWLycnJCY9CHkRcU5KelyQOKBfkG8SLjV7kqdpP3ZXpyMKiwlh8aDELDy1k1YlVxFvjbfuKFSpG+8rt6VC5Aw9VfIgibkWy/foiIulRki4iIrmeq2vKfutgTvvm4WEm5Nu3m8ubb0LVqtCjBzz2GFSrZp94JXdwcHDAyUl/6uQVDhYHLFjoVLUTgxsOpkXZFtk+eNyZ8DMsPLiQBQcXsOH0BtvUcAC1/GrxaJVH6RDUgQYlGuSbaeFEJO/Rby4REcmTChWCTZsgLAyWLIGff4bly+HQIRgzxmwu//339o5S7G1ww8GsP73e3mEUWGtOriEyNjLd/Q4WB6yGleKFijOowSCerf8sJQpnb/+VsKgw5u03B6TbcnZLin0NSjSga7WudKnWhcq+lbP1uiIiWaU+6SIikm+Eh5sJ+7x5MHAgdOhgbt+7F3r1gieeMF9Ll7ZvnJIzrFYrJ/4bgbB8+fI4OKgfcU6r/WVt9l7Ym2q7k4MT8dZ4mpVuxpBGQ+hUtRPOjs7Zdt2ImAgWH1rM93u/Z8XxFVgNK2AOSNesTDO6VutK52qdKeNdJtuuKSJyK+qTLiIiBZK3Nzz5pLkkN2+emaiPGAEjR5pN559+Grp00Vzs+Vl8fDzfffcdACNGjMDFxcXOERVsFsym625ObvSp04dBDQZRw69Gtp0/NiGW347+xg/7fuCXw79wI/6GbV+jko14otYT9KjRgwDPgGy7pojI3aAkXURE8r2XX4Zy5WD2bFi7FlauNJfnn4euXWH8eChe3N5RSnazWCz4+/vb1sW+KvtWvisDwe27sI/pu6Yz++/ZXLp2yba9im8VetXqxeO1HqeST6Vsu56IyN2m5u4iIlKgnDwJ330H334LR4+Cjw+cP28OTgdw44Y51ZuI3LnXV7zOsX+PMajBIFqWbZltD0vCb4QzZ98cpu+ezrZz22zbAz0DeaLWEzxR6wnqBtTVwxkRyTU0T/otKEkXEREw52LfutVM2h97LGlbtWpQqZLZp71dO9Dg4CK5g2EYrD+9nm92fsP8A/O5Hn8dMPu3PxL0CP3q9iO4UjBODvpPKyK5j/qki4iI3IbFAo0bm0uinTvh8GFzWboUSpaEfv3M+dg12JyIfUTGRDL779l88dcX7L+437a9WrFq9Kvbj6fueQo/Dz87Rigikr1Uky4iIpLMkSMwdSrMnAmX/uve6uBgjhT/zjtQt65dw5NMiIuL4/v/5uHr1asXzs7ZN3q43H0HLh7gi7++4Ns939qmcfNw9uDxmo/Tr14/GpVspObsIpJnqCZdREQki4KC4KOPYOxYWLQIpkyB1avNqd1eesne0UlmGIbBqVOnbOuS+8Vb4/n50M98/tfnrD652ra9im8Vnm/wPL3v6Y23m7cdIxQRufuUpIuIiKTB1dXsq/7YY2bz959+glatkvaPHQvR0TBoEJQqZbcw5RacnJzo1q2bbV1yr8iYSL7Z+Q2Ttk7idPhpABwsDnSs0pFBDQbxQPkHVGsuIgWGmruLiIhkUlSUmZiHh4OjozmN27Bh0KCBvSMTyVvORpzl062fMmXHFMJjwgEoXqg4z9Z7loH3DqSMdxk7Rygikj3U3F1EROQucnc3+6x/8gmsWQPz5plL69bw+uvQpo05MJ2IpG1P6B4+3vwxP+77kXhrPABVi1XllSav8GTtJ3Fz0jyIIlJwqSZdRETkDuzZAxMmwA8/QLyZa/DeezBihH3jErBarZw9exaAUqVK4eDgYOeICjbDMFhzcg3jNozjz+N/2ra3LNuSYfcNo33l9jhY9G8kIvlTZmrSdScUERG5A/fcA7NmwbFj8OKL4OUFjz+etD80FGJi7BdfQRYfH8+MGTOYMWMG8YlPUCTHGYbBH//8QfMZzWn9bWv+PP4nDhYHetboybb+21jTZw0PBz2sBF1E5D92vxtOmTKF6tWr4+PjQ9OmTdm4ceMty8+ZM4dGjRpRrFgxKlSowMCBA7l8+XIORSsiIpK2MmVg0iQICYFy5ZK2/+9/UKECTJ4MN27YK7qCyWKx4OPjg4+PjwYdswPDMFhyeAmNpzWm7fdt2XhmIy6OLjx/7/P8M/gf5nSbQ4OSGshBRORmdm3uPn/+fPr378+kSZNo3Lgx06ZNY9asWezYsYPSpUunKr9p0yaCg4P54IMPaN++PefPn2fIkCFUqlSJOXPmZOiaau4uIiI5JSoKatSA0+Zg1ZQsCSNHQr9+5ujxIvmR1bCy6OAixq4fy+7Q3QC4O7kzsP5AXm36KiUKl7BvgCIidpBnmrtPnjyZ3r1706dPH6pWrcpHH31EqVKlmDp1aprlt23bRtmyZXn++ecpV64c9913H/369WPnzp05HLmIiMjteXrC0aPw1VfmaPDnzplTtlWubG6LjbV3hCLZxzAMfj70M/d8dQ/dfurG7tDdeDh78Np9r3Fy6Ekmtp2oBF1EJAPslqTHxsaya9cuHnjggRTbW7duzdatW9M8pnHjxpw7d47ff/8dwzAICwtj8eLFtG3bNt3rxMTEEBERYVsiIyOz9XOIiIjciosLDBwI//wDn38OJUrAmTNmM/hvvrF3dCLZY+XxlTSe1phOczux78I+vFy9eKP5G5waeooPHvwAPw8/e4coIpJn2C1Jv3z5MgkJCfj5pbxp+/v7ExYWluYxjRs3Zvr06fTu3ZsiRYpQoUIFvL29+fjjj9O9zvjx4wkMDLQtQUFB2fo5REREMsLVFZ5/3hxg7tNPoW5d6NMnaX9oKFitdgsvX4qPj+eHH37ghx9+0MBxd8mWs1t44NsHaDO7DdvObaOQcyFGNhvJyRdP8m7rd/Et5GvvEEVE8hy7Dxx380AuhmGkO7jLwYMHGTZsGK+//jobNmxg8eLFnDx5kiFDhqR7/mHDhhESEmJbjhw5kq3xi4iIZIabGwweDDt2QKFC5raEBHjoIWjYEFatsm98+YnVauXo0aMcPXoUq56AZKu9YXvpNKcTTaY1YdWJVbg4ujCk4RCODznO/z3wfxR1L2rvEEVE8iwne13Y19cXR0fHVLXmFy5cSFW7nmj8+PE0adKEl156CYBatWrh4eHBgw8+yOjRowkMDEx1jKurK64anUdERHKZ5M+jDxyAEyfMgeYeeACCg+GDD8zp3STrHB0defTRR23rcufORpxl1KpRzN4zGwMDB4sDve/pzVst36JskbL2Dk9EJF+wW026i4sLdevWZdVNVQarV6+mUaNGaR5z/fp1HBxShqxfuiIiktfVqmU2gx88GJyc4I8/zObwTz0FJ0/aO7q8y9HRkTp16lCnTh39vXCHomKjGL16NEGTg/h2z7cYGHSr3o39z+9n+qPTlaCLiGQjuzZ3Hzx4MDNnzmTWrFkcOnSI1157jTNnztC/f38ARo8ebVsHaNeuHT///DNTp07lxIkTbN68mWHDhnHvvfemWYsuIiKSV/j5mX3VDx2Cnj3BMOC776BKFfj7b3tHJwVVgjWBaTunUXlyZd5d9y7X46/TrEwztvbfyk/df6Jqsar2DlFEJN+xW3N3gG7dunHlyhXef/99QkNDqV69OgsXLqRMmTIAhIaGcvbsWVv5p556iqioKL7++mtGjBiBt7c3LVu2ZOzYsfb6CCIiItmqYkWYMweGDYPhwyEmxqxpl8yzWq1cuHABAD8/v1St8eTWVhxfwSvLX+HvMPMpUYWiFfiwzYd0qdYl3fGDRETkzlmio6MNeweRkyIiIggMDCQ8PPy2k8iLiIjYk2FAZCQk/rqKiIDHH4dRo+C+++wbW14QGxvLuHHjABgxYgQuLi52jihvOHr5KC/98RJLjy4FoIhbEd5s8SaDGgzC1Unj/IiIZEVERATe3t6EhITcNg/VI2UREZFcymJJStAB3n8fli2Dpk2hVy9I1thM0mCxWChcuDCFCxdWzW8GRMdGM3LlSGp+WZOlR5fi5ODEkIZD+GfwP7zc5GUl6CIiOUQ16SIiInlEWJhZiz59ulnLXqgQvP46vPaaOQ+7SFYYhsGCgwt4+Y+XORNxBoC2ldoyKXgSVYpVsXN0IiL5g2rSRURE8iF/f/jmG9i+HZo1g2vXYPRos8/6ihX2jk7yokOXDvHQdw/R/afunIk4Q7ki5VjcczHLnlimBF1ExE6UpIuIiOQx9erBunXwww8QGAhHj8KMGfaOSvKSqNgohv85nNpf1mbF8RW4OroyusVoDjx/gEerPqruASIidmTX0d1FREQkaywWcxC59u1h7Fh45ZWkfeHh4OkJBX1q8Pj4eBYtWgRA586dcXLSnz0Avxz+hUHLBnE2whzU4JGgR5gYPJGKPhXtHJmIiIBq0kVERPI0b2/46CMICEja1rcvNGwIf/1lv7hyA6vVyoEDBzhw4ABWq9Xe4djd+cjzdJvXjUfnPMrZiLNUKFqBXx//lV8e/0UJuohILqJHyiIiIvnIuXOwahVcvQqNGsGgQfDee1C4sL0jy3mOjo60a9fOtl5QWQ0rU3ZMYfiK4UTEROBoceTV+17lzZZvUsi5kL3DExGRm2h0dxERkXwmLAyGDYPvvjPflykDX38NbdvaNy7Jefsv7GfArwPYdGYTAA1LNmTqI1Op7V/bzpGJiBQsGt1dRESkAPP3h9mz4c8/oXx5OH0a2rWDp582a9gl/7sRf4M3V71J3a/rsunMJjxdPJncbjKb+m5Sgi4iksupubuIiEg+1aYN7N0Lb74JkybB2rUFazA5wzC4cuUKAD4+PgVmxPKtZ7fyzM/PcPDSQQA6VunIZ+0+o7R3aTtHJiIiGaEkXUREJB/z8IAJE6BnT4iJSeqbbrXCxYtmrXt+FRcXx2effQbAiBEjcHFxsXNEd9eN+Bu8tfotxm8ej9WwEuAZwGftPqNLtS4F5gGFiEh+oObuIiIiBUCjRtCiRdL7qVOhShWYOROMfDw6jaurK66urvYO467bcnYLdb+uy4ebPsRqWHmy9pPsf34/Xat3VYIuIpLHaOA4ERGRAsYwIDjY7LMO0LGjObBc8mncJG+4EX+D0atH8/Hmj221518//DUdq3S0d2giIpKMBo4TERGRdFkssGwZjBsHzs7wyy9QsybMn2/vyCQzEmvPP9r0EVbDytP3PM3+5/crQRcRyeOUpIuIiBRATk7w+uuwfTvccw9cvgzdu8MTT8B/Y61JLhWbEMuolaNoOr0phy4dItAzkF8e+4VZnWbh4+5j7/BEROQOKUkXEREpwGrXhm3b4I03zJHf586FI0fsHVX2iI+PZ/HixSxevJj4+Hh7h5MtDl48SJNpTXhvw3tYDStP1X6K/c/v55Eqj9g7NBERySYa3V1ERKSAc3GBd9+FRx4xE/bGjZP2GYbZPD4vslqt7NmzB4D27dvbOZo7YxgGn//1Oa/++So34m/g4+7DlIen0LV6V3uHJiIi2UxJuoiIiADQsKG5JDp4EB5/3BwJvkED+8WVVY6OjrRp08a2nledjzzPMz8/w/JjywEIrhjM9EenU6JwCTtHJiIid4OSdBEREUnT8OGwZw/cdx+MGQOvvWY2ic8rHB0dadq0qb3DuCPzD8xn4K8DuXL9Cm5Obnz04EcMajBI06qJiORj6pMuIiIiaZo1yxxMLj4eRo6E1q3h9Gl7R1UwRMRE0Htxb7r/1J0r169QL7AeOwfs5IWGLyhBFxHJ55Ski4iISJqKFjUHkpsxAzw8YN06cyT4efPsHVnGGIZBREQEERERGIZh73AybNu5bdT5qg7f7vkWB4sDo5qPYnO/zVQrXs3eoYmISA5Qki4iIiLpsligTx/Yvdvsr371KvTsCYsW2TmwDIiLi2PixIlMnDiRuLg4e4dzW1bDykcbP6Lp9KacuHqCst5lWddnHWNbj8XF0cXe4YmISA5Rn3QRERG5rUqVYMMGs2/66tXmSPB5gYND3qiPCIsKo/fi3vxx7A8AulfvzpRHplDErYh9AxMRkRxniY6OznT7r9mzZ9O1a1cKFSp0N2K6qyIiIggMDCQ8PBwvLy97hyMiIpLnxMeD03+P+WNjYc4ceOqpvDtVm739eexPnlr0FGHRYbg7ufNJ20/oX6+/+p6LiOQjEREReHt7ExIScts8NEuPl9966y0qVKjA//73P7Zs2ZKlIEVERCRvckrWDm/4cOjdGx59FC5ftl9MeVFcQhyvr3idh757iLDoMGr61WT7gO08W/9ZJegiIgVYlpL0o0ePMm3aNK5evUq7du2oW7cuH3/8MaGhodkdn4iIiORilSuDiwssWQJ168LGjfaOKG848e8Jms9ozgcbPwDgufrPsa3/NqoXr27nyERExN6y1Nw9uQsXLjBnzhy+++47jhw5woMPPkjv3r1p3759ruwHpubuIiIi2WvXLnMwuaNHzXnUx44151S3958B8fHx/PGH2cc7ODgYJ6fcMRTPvP3zeHbJs0TERFDErQjfPPINXat3tXdYIiJyF9315u7J+fn50aRJExo1aoSDgwP79+9n4MCB1KxZk3Xr1t3p6UVERCSXq1sXduyAJ56AhAQYMQLat4cLF+wbl9VqZfv27Wzfvh2r1WrfYICY+BheWPYCPef3JCImgqalm7J74G4l6CIikkKWk/SwsDAmTZrEvffeS9u2bYmIiGD+/PkcOHCAf/75h44dOzJgwIDsjFVERERyqcKF4bvv4JtvwN0dNm+GyEj7xuTo6EjLli1p2bIljo6Odo3l5NWTNJ/RnM//+hyAEc1GsKbPGsoWKWvXuEREJPfJUnP3bt26sWLFCipVqkSfPn144okn8PHxSVEmJCSEypUrExUVlW3BZgc1dxcREbm79u2D06fN2nSBJYeX8PTip7l64yo+7j7M7jyb9pX1wxERKUgy09w9S52zihcvzh9//EGjRo3SLRMQEMCBAweycnoRERHJw2rWNJdEK1fCpEkwcyb4+torqpwXb41n1MpRfLjpQwAalWzEvO7zKONdxs6RiYhIbpal5u7NmjWjTp06qbbHxsby/fffA2CxWChT5va/hKZMmUL16tXx8fGhadOmbLzNsLAxMTG8/fbbVK1alaJFi1KzZk1mzZqVlY8hIiIid1lcHPTrB7/+CvXrw/btOXdtwzC4ceMGN27cwDDuaJzcTDsfeZ7Ws1rbEvQhDYew7pl1StBFROS2stTcvXDhwhw7dgw/P78U2y9fvky5cuWIzGAntPnz59O/f38mTZpE48aNmTZtGrNmzWLHjh2ULl06zWN69OjBhQsXGD16NBUrVuTixYvEx8fTuHHjDF1Tzd1FRERy1t9/Q9eu8M8/5nRtn34KAwbA3Z4KPDY2lnHjxgEwYsQIXFxc7u4F/7PqxCoeX/A4F6IvUNilMNMfnU636t1y5NoiBZnVaiU2NtbeYUgB5uLiku4MZ3e9ubthGFjS+M167tw5vL29M3yeyZMn07t3b/r06QPARx99xMqVK5k6dSpjxoxJVX758uVs2LCBffv22frAly2rAVdERERys9q1zRr0Pn1g8WJ47jlzPvWvvoJChewdXfaxGlbeW/8eb615C6thpbZ/beZ3n09l38r2Dk0k34uNjeXEiRO5YiYHKbgcHBwoX778HT8UzlSS3qRJEywWCxaLhQ4dOqSYbzQhIYFTp07x4IMPZuhcsbGx7Nq1i1deeSXF9tatW7N169Y0j1m2bBl169Zl4sSJ/Pjjj3h4eNC+fXtGjx6Nu7t7msfExMQQExNje5/RWn4RERHJPt7esHAhfPwxvP46zJ5tzq++fj0UKXJ3runs7Mwbb7wBkG7NRna5cv0KvRb24vd/fgegX91+TG43GXfntP8+EZHsYxgGISEhODo6Urp06bv+/10kLVarlfPnzxMSEkKZMmXSrNTOqEwl6Y888ggAf//9N23atMHT09O2z9nZmbJly9KpU6cMnevy5cskJCSkajLv7+/PihUr0jzmxIkTbN68GTc3N+bMmcOlS5d46aWX+Pfff/nqq6/SPGb8+PG89957GYpJRERE7h6LBYYNgwYNoGdPc371TDTAy8L1LDky9drfYX/TeW5njv97HHcnd77s8CW96/S+69cVEVN8fDzXrl2jRIkSFMpPzXMkzylevDjnz58nPj4eZ2fnLJ8nU0n6yJEjAShTpgzdunXDzc0tyxdOdPMThvSa0oP5dMJisTB9+nRbs/qYmBh69erFxIkT06xNHzZsGIMHD7a9j4yMJCgo6I7jFhERkaxp2dKsRff2TuqXHhkJbm5wB3/T2MXcfXPp+0tfrsVdo3yR8izquYh7Au6xd1giBUpCQgJAjo07IZKexO9gQkJCziXpiZ588sksXzCRr68vjo6OhIWFpdh+4cKFVLXriQICAihRokSKfu9VqlTBMAzOnTtHpUqVUh3j6uqKq6vrHccrIiIi2ScwMGndaoUnnoCrV+GnnyAgIHuukZCQwMqVKwF44IEHsrVWPcGawIiVI/ho00cAPFTxIX7s+iM+7j7Zdg0RyZw7aV4skh2y6zuY4Q4bpUqV4tKlSwCULFmSUqVKpbtkhIuLC3Xr1mXVqlUptq9evTrd+debNGlCSEgIUVFRtm3//PMPDg4OlCxZMqMfRURERHKRI0dg3TrYsMGcpm3Lluw5b0JCAps3b2bz5s22mrbscPnaZdp9386WoA9vOpxlTyxTgi4iItkiwzXp77//PoULF7atZ8dTgsGDB9O/f3/q1q1Lo0aNmD59OmfOnKF///4AjB49mvPnz/PNN98A5vRr77//Ps899xyjRo3i8uXLjBo1iqeffjrdgeNEREQkd6taFbZtg86d4eBBaNECPvvMnKbtTjg6OtKkSRPbenbYE7qHznM7c+LqCQo5F2LGozPoUaNHtpxbRCQtFouFRYsWZXjsr8xq1aoVderUYdKkSXd0nrfffpvFixeze/fuDB9Trlw5hg4dytChQ+/o2vlNluZJz05Tpkxh4sSJhIaGUr16dT744AOaNWsGwIABAzh9+jS///67rfzhw4d55ZVX2LJlCz4+PnTp0oW33norw0m65kkXERHJnSIjzWnaFi403/fvbybruaXX2px9c+j7c1+ux1+nQtEKLO65mFr+tewdlkiBd+PGDU6cOEH58uWzZcysnNSnTx+uXr3K4sWL0y0TGhpK0aJFM9WFNzY2lhIlSjB06FDbLBfJjRs3jo8//pjz588TFRWFs7OzrUI2q6KiooiJicHX1zfDx1y8eBEPD498M+Dfrb6LmZknPcNJekRERIaDy83Jr5J0ERGR3Msw4P33YdQoc71rV5g/374xxVvjGbFiBOM3jwcguGIwP3T9Qc3bRXKJ/Jqkx8bG3tFgeEOHDuXXX3/l6NGjqVpBBwUF0aFDByZOnHjb89xpHAVJdiXpGe6TXqJECUqWLHnLJbGMiIiISFZYLDBiBCxbZg4uN3x41s9lGAYJCQkkJCRgGFlrOJjY/zwxQR/RbARLn1iqBF1Esl2rVq144YUXePnllylWrBgPPvggYDZ3T0ziY2NjeeGFFwgMDMTNzY1y5coxbty4NM/Xr18/jh07xrp161JsX79+PUePHqVfv3626yZvbl6uXDnGjh1Lnz598Pb25tlnnwVg6tSplC5dmkKFCtG5c2cmTJhAkSJFbMe9/fbb1KlTx/a+T58+dOrUifHjxxMYGIivry+DBg0iLi4uxbWSN7O/evUqAwYMwN/fHzc3N2rWrMmvv/4KmFN4P/7445QqVYpChQpRq1Ytfvzxx0z9jPOKDPdJ/+233+5mHCIiIiI2bdvC8ePmtGyJDh40+69ndFicuLg42x+vI0aMyHRN0O7Q3XSe25mTV0/i4ezBzE4z6Va9W6bOISI5zzAMrsVds8u1CzkXuqOxu2bNmsX//vc/Nm7cmObDxU8//ZRffvmFefPmUaZMGc6cOcOZM2fSPFetWrVo0KABM2bMoGXLlrbt06dPp2HDhtSsWTPdOD766CPefPNNW1P5jRs38txzz/HBBx/QsWNHVqxYwZtvvnnbz7N69WoCAwNZvXo1//zzDz179qROnTq2xD85q9VKu3btiIyM5LvvvqNixYocOHDANqbIjRs3qF+/PsOHD8fLy4ulS5fy1FNPUaFChXQHHs+rMpykN2/e/G7GISIiIpJC8gR950647z7o0QO++grudvfFH/f+SL9f+nE9/joVi1Zk8WOLqemX/h+0IpJ7XIu7huc4T7tcO2pEFB4uHlk+vlKlSnz44Yfp7j99+jSVK1emWbNmWCwWypYte8vz9e3bl2HDhvHZZ5/h6elJVFQUP/30ExMmTLjlca1bt2bYsGG292+88Qbt2rWzbQsKCmLTpk22Wu70FC1alM8++wxHR0eqVq1Khw4dWLlyZZpJ+ooVK9i2bRsHDx4kKCgIgAoVKtj2lyxZMkVMgwcP5vfff+enn37Kd0l6hpu77927F6vValu/1SIiIiKSnfbsgfh4mD0bmjWDkydvf4yzszPDhw9n+PDhODs7Z+g68dZ4hi0fxhMLn+B6/HXaVmrLX8/+pQRdRHLEvffee8v9ffr0Yffu3VSpUoUhQ4awfPly277nnnsOT09P2wLw+OOPY7VamTt3LgBz587FMAwee+yxTMVx+PBhGjZsmGLbze/TUqNGjRSzawQGBnLhwoU0y+7evZtSpUrZEvSbJSQk8H//93/Url0bX19fPD09Wb58OadPn75tHHlNhmvSmzRpwvHjx/Hz86NJkyZYLJY0m2BYLBYiIyOzNUgREREp2J55BsqXN2vSd+2Ce++FOXOgTZv0j7FYLJkaROrStUs8Nv8xVp5YCZj9z9+9/10cHbJn+jYRyRmFnAsRNSLKbte+Ex4et66Fr1evHidOnOC3335jxYoV9OjRgzZt2jB//nzGjBmToqYZwNvbm27dujFjxgz69evHjBkz6Nat220HLrs5DsMwUjXjz8hYHzc/ILVYLLaK35vdbraujz/+mIkTJzJp0iRq1aqFh4cHQ4cOJTY29rZx5DUZTtIPHDhA8eLFbesiIiIiOalVK9ixA7p0ge3bITgYxo2DV1/NeD/19OwK2UXnuZ05FX5K/c9F8jiLxXJHTc5zOy8vL3r27EnPnj3p1q0bbdu25cqVK/j5+eHn55eqfL9+/WjVqhW//vorGzdu5L333sv0NatWrcq2bdtSbNu+fXuWP0NaateuzdmzZzly5Eiatenr16/n0Ucf5cknnwTMPuxHjx6lWrVq2RpHbpDhJL1MmTJprouIiIjklNKlYf16GDQIpk83R38vUwbSarmZkJDA+vXrAXNsneRNLpP7Ye8P9P+lP9fjr1PJpxKLey6mhl+Nu/kxRESyZOLEiQQGBlKnTh0cHBz46aefCAgISDHK+s1atmxJpUqVePrpp6lUqRItWrTI9HUHDx5MixYtmDBhAo888girVq3it99+u6NB8tKKs0WLFnTt2pUJEyZQqVIlDh06hMVioW3btlSqVIkFCxawadMmihYtyoQJEwgNDc2XSXqG+6Tf7MiRI7z88su0b9+eDh068PLLL3PkyJHsjE1EREQkFTc3+OYb+Pxz6NQJundPu1xCQgJr165l7dq1JCQkpNofb43n5T9eptfCXlyPv067Su3Y1n+bEnQRybU8PT354IMPuPfee2nQoAEnT55k2bJlODjcOq3r27cv//77L3379s3SdZs2bcpXX33FhAkTuOeee/j999956aWXsn1e+gULFtCgQQMef/xxqlevzmuvvWa7f7/55pvUq1eP4OBgWrVqRUBAAJ06dcrW6+cWlujo6ExPHLpo0SL69OlDvXr1bAMG/PXXX+zYsYMZM2bQpUuXbA80u0RERBAYGEh4ePht+2KIiIhI7mYYSU3db9wwm8E3a2a+j4+P548//gAgODgYJ6ekBoQXoy/y2ILHWHViFQCjmo/inVbvqP+5SB5048YNTpw4Qfny5bM9aZT0Pfvssxw6dMjWYklu/V2MiIjA29ubkJCQ2+ahGW7untwbb7zBsGHDUs2NN3bsWN58881cnaSLiIhI/pGYoBsGPPecOfp7Yj91JycnOnTokOqYnSE76Ty3M6fDT+Ph7MG3nb+lSzX97SIicivjx4/nwQcfxMPDg99++41Zs2bxxRdf2DusfClLzd3DwsJ44oknUm1/7LHHCAsLu+OgRERERDIjIQGcnMBqNfupP/YYREenLvfd39/RdHpTToefprJPZbb236oEXUQkA7Zt28aDDz5IrVq1+Oqrr/j000/p37+/vcPKl7JUk968eXM2btxIxYoVU2zftGkT9913X7YEJiIiIpJRTk4wdao5NduQITBvHhw8CIsWQcWKZv/zV5e/yqStkwBoX7k933f5niJuRewat4hIXjFv3jx7h1BgZDhJX7p0qW29Q4cOvPnmm+zevZsGDRoAZp/0hQsX8sYbb2R/lCIiIiK3YbGYTd5r1YKuXeHQoVhmzfoAR0dYV2YNq06b/c/fbPEmb7d6GwdLlsfPFRERuWsyPHCcp6dnxk5osRAZGXlHQd1NGjhOREQk/zt3Dnr2jOXBB8cB8H8xk3AtHM+3nb6lc7XOdo5ORLKTBo6T3CLHB46LiorKWqQiIiIiOaxkSXhmwjyGveJPQqUllK/nx6LHFlG9eHV7hyYiInJLWeqTLiIiIpJbxSXEMWz5MD7d9im0gYeDHua7ztvwdvNm9WooXRoqVbJ3lCIiImnLcpIeHR3N+vXrOXv2LLGxsSn2Pf/883ccmIiIiEhmXYi+QI+ferD21FoARrcYzVut3sLB4sDRo9C5s9l3/ccfoW1bOwcrIiKShiwl6bt376ZLly5cv36d6OhoihYtyuXLlylUqBDFixdXki4iIiI5bvv57XSZ24UzEWco7FKYmR1n4n/Vn82bNtO4cWM8PBypVg22bIH27eH//g9efz1prnUREZHcIEvDmr7++uu0b9+es2fP4u7uzpo1azh06BB169blvffey+4YRURERG7p2z3f0mx6M85EnCHIN4it/bfycOWHWbFiBStWrCAhIYESJWDNGhgwAAwDRo6E7t1Bw+6IiCRZs2YNFouFq1ev3rVrWCwWFi9efMfnadWqFUOHDs1w+ZMnT2KxWNi9e/cdX/tuylKS/vfffzNkyBAcHR1xdHQkJiaGUqVKMXbsWN5+++1sDlFEREQkbXEJcQz5bQi9F/cmJiGGR4IeYVv/bVQrXg0HBwfuuece7rnnHhwczD95XF3h66/NxdkZFiyAxo3hn3/s/EFEpMDp06cPFouF999/P8X2xYsXY8lkE59y5coxadKkbCl33333ERISgre3d6Zi2LFjBxaLhQ0bNqS5Pzg4mI4dOwIQEhJCu3btMnX+tCxcuJB33303w+VLly5NSEgINWvWvONr301ZStKdnZ1tXxw/Pz/OnDkDgJeXl21dRERE5G66EH2BNrPbMHnbZADeavkWix9bjLeb+Yelk5MTnTp1olOnTjg5pezhN2AArF0LgYGwfz988UWOhy8igpubGx988AH//vuvvUMBIC4uDhcXFwICAjL9oKB+/frcc889zJgxI9W+M2fOsGLFCvr16wdAQEAArq6ut4wjI3x8fChcuHCGY3R0dCQgICDV74TcJktJeu3atdm5cycALVq0YOzYscyZM4fXXnuNGjVqZGuAIiIiIjf769xf1J9Sn3Wn1lHYpTA/P/Yzb7d6GwdLxv+0adIEduyAF16AmyqyRERyRJs2bQgICGDcuHG3LLdgwQJq1KiBq6sr5cqV4+OPP7bta9WqFadOneKll17CYrFkKrm2WCx89dVXPProo3h4eDB27NhUzd1PnTrFI488QtGiRfHw8KBGjRosW7YszfP169ePefPmER0dnWL7zJkzKV68OB06dLBdN7G5e2IT9Hnz5tGqVSvc3Nz47rvviI+PZ8iQIRQpUgRfX1+GDx9O79696dSpU4rPnry5e7ly5Xjvvffo27cvhQsXpkyZMkyZMsW2P63m7vv376dDhw54eXlRuHBhmjdvzrFjxwD466+/ePDBBylWrBje3t60bNnSlgffTVlK0t955x0CAgIAePPNN/Hx8WHo0KFcvHiRyZMnZ2uAIiIiIslN3zWd5jOaczbiLFV8q7Dt2W10rNIxS+cKDITJk8HFxXwfHw9jx0JkZDYGLCJ2ER2d/nLjRsbLXr+esbJZ4ejoyHvvvcfkyZM5e/ZsmmV27NhBjx49eOyxx9i7dy9vv/02b775JjNnzgTMJt+lSpVizJgxhISEEBISkqkY3nrrLR599FH27t1L3759U+0fNGgQMTExrFu3jr179/LBBx/g6emZ5rl69epFXFwcP/30k22bYRjMnDmT3r1737IGe/jw4QwZMoSDBw8SHBzMBx98wPfff8+MGTPYuHEjERERGerH/vHHH3Pvvfeya9cunn/+ef73v/9x6NChNMueO3eOFi1a4ObmxqpVq9ixYwd9+/YlPj4egMjISHr37s369evZsmULlStXpn379kTe5V8SWarnr1evnm29ePHiLFq0KNsCEhEREUlLbEIsQ38fypfbvwTg0SqPMqvTLFvz9lTlY2OZMGECAC+//DIuiZn4LbzxBnzwgTlF2+LFULlytoUvIjksnTwSMGd4WLo06b2fH1y7lnbZli3NQScTlSsHly6lLmcYWYkSOnfuTJ06dXjrrbeYNm1aqv0TJkzggQce4M033wQgKCiIAwcO8NFHH9GnTx98fHxwdHSkcOHCtorUzHjiiSdSJOcnTpxIsf/06dN07dqVWrVqAVChQoV0z+Xj40OnTp2YMWMGffr0AcyB6I4fP57mA4Dkhg4dSpcuXWzvJ0+ezIgRI+jcuTMAn332Wbo1+Mm1b9/eNtvY8OHDmThxImvWrKFq1aqpyn7++ed4e3szZ84cnJ2dAfPnm6h169Ypyn/99dcULVqUtWvX8vDDD982lqzKUk16ogsXLrBx40Y2bdrExYsXsysmERERkRTOR57n/ln38+X2L7Fg4d3732Vhz4XpJuiJYmJiiImJyfB1OnUya9cPHIAGDVL+ES8icrd88MEHzJo1iwMHDqTad/DgQZo2bZpiW9OmTTl69CgJCQl3fO177733lvuHDBnC2LFjadq0KW+99RZ///23bV+NGjXw9PTE09PTNhBcv379WLduHf/8NyLn9OnTadq0KVWqVMlwHOHh4YSFhdGwYUPbNkdHR+rXr3/bz1O7dm3busViISAggAsXLqRZdvfu3TRv3tyWoN/swoULPPfccwQFBeHt7Y23tzdRUVGcPn36tnHciSzVpEdERPDSSy8xf/582xfD0dGRrl27MnHixEyPBCgiIiKSno2nN9Ltp26ERoXi7erND11/oH3l9rc9ztnZmRdeeMG2nhGNG5v91Lt3h40b4ZFHYMwYc7o2hzuq2hCRnHar6RUdHVO+TyeHA1L/3z95MsshpatFixYEBwczcuRIWw10IsMwUvUzN7JabZ8GDw+PW+7v378/wcHBLF26lOXLlzNu3Dg+/vhjBg8ezLJly2yDvLm7uwNmP/uyZcsyc+ZMXnvtNRYuXMhnn32WpTiy8rlvvt9bLBasVmuaZRNjTk+fPn24ePEikyZNomzZsri6utKkSRNiY2NvG8edyNKvm0GDBrF9+3bmz5/P+fPnCQkJYf78+ezatcv2y1BERETkThiGwRd/fcH9s+4nNCqUmn412T5ge4YSdDD/MPP19cXX1zdTAykFBsKqVfC//5nNV998E7p2VT91kbzGwyP9xc0t42VvzuPSK3en3n//fZYsWcKmTZtSbK9evXqqac02bdpEUFAQjv89bXBxccmWWvX0lC5dmueee46FCxfyyiuvMHXqVADKli1LpUqVqFSpEiVLlgTMe+8zzzzDrFmz+OGHH3BwcKBHjx6Zup63tzf+/v5s27bNti0hIYFdu3Zl34fCrHVfv359uqPJr1+/niFDhtC+fXvbwH2X0urrkM2ylKT//vvvfPnllzz44IO2UfAefPBBPvvsM37//ffsjlFEREQKmBvxN+j3Sz8GLRtEnDWOHjV6sLnfZir5VMqR67u4mNOyffONub58OZw6lSOXFpECqlatWvTq1SvVQNyvvPIKK1eu5N133+XIkSPMmjWLzz77jGHDhtnKlCtXjnXr1nHu3LlsTyKHDh3KH3/8wYkTJ9i5cyerVq2iWrVqtzzmmWee4fz584wcOZLHHnvstrX1aRk8eDDjxo3j559/5vDhw7z44ov8+++/mZ4a7lZeeOEFIiIieOyxx9i+fTtHjx5l9uzZHD58GIBKlSoxe/ZsDh48yNatW+nVq9dta9+zQ5aSdB8fH7y8vFJt9/LyokiRIncak4iIiBRgZ8LP0HxGc2bsnoGDxYEP23zInK5z8HS5xShQaUhISGDbtm1s27YtyzVM/frBunXw/fdQs2aWTiEikmHvvvtuqibd9erVY968ecyZM4eaNWsyevRoxowZk6JZ/JgxYzh58iQVK1akePHi2RpTQkICgwYNolq1arRt25YqVarwxRdf3PKYMmXK0KZNG/7999/bDhiXnuHDh/P444/z9NNP06RJEzw9PQkODsbt5mYQd8DX15dVq1YRFRVFy5YtqV+/PlOnTrU1mZ8+fTr//vsvdevW5amnnmLIkCH4+fll2/XTY4mOjs50h4bp06ezcOFCpk6dSmBgIAChoaEMGDCARx991DZJfW4UERFBYGAg4eHhaT5oEBEREftZc3INPX7qwcVrF/Fx92Fut7m0qdAmS+eKjY21zT08YsSIDI3unhGbNpnN4dVPXSR3uHHjBidOnKB8+fLZmsBJ7mK1WqlWrRo9evTg3XfftXc4abrVdzEiIgJvb29CQkJum4dmeOC4Jk2apGhacOzYMapVq0bp0qUBOHPmjK2Nfm5O0kVERCT3MQyDSVsm8eqfr5JgJFA3oC4Ley6kXJFyWT6ng4MD1atXt61nh4gI6NYNQkJg+3b49lvQM38Rkex36tQpli9fTsuWLYmJieGzzz7jxIkTPPHEE/YO7a7LcJL+yCOP3JUApkyZwqRJkwgNDaVatWp8+OGHqaYYSMvmzZsJDg6mevXqbNmy5a7EJiIiIndfdGw0A34dwA97fwDgqdpP8fXDX+PufGf9/pycnOjevXt2hGjj5QX/93/w3HPw88/QqJE5n/ptZhYSEZFMcnBwYObMmQwbNgzDMKhZsyYrVqy4bX/4/CBLzd2zy/z58+nfvz+TJk2icePGTJs2jVmzZrFjxw5bDX1awsPDadq0KRUqVODChQuZStLV3F1ERCT3OHzpMF3ndWX/xf04WhyZGDyRFxq+kK0DA90N27ZBly5w7pyZuM+eDR072jsqkYJJzd0lt8iu5u531PZr165d/Pjjj8yZM4fdu3dn+vjJkyfTu3dv+vTpQ9WqVfnoo48oVaqUbUj/9AwZMoQePXrQqFGjLEYuIiIi9jb/wHwaTG3A/ov7CfAMYFXvVQxuNDjXJ+gADRua86k3b242gX/0UXjnHUhnKl4REZEMy1KSfuHCBdq1a0fz5s159dVXeeWVV2jWrBnt27fn4sWLGTpHbGwsu3bt4oEHHkixvXXr1mzdujXd47799luOHz/OyJEjM3SdmJgYIiIibEukJjkVERGxq7iEOF7+42W6/9SdyNhIWpRtwa6Bu2hRtkX2XicujgkTJjBhwoR058C9E/7+sGIFvPCC+X7fPsgDzxdE8q2bR0UXyWnZ9R3MUpI+bNgwIiMj2b59O2fPnuXcuXP89ddfREZGppiv71YuX75MQkJCqiHs/f39CQsLS/OYf/75h9GjRzN9+nScnDLWnX78+PEEBgbalqCgoAwdJyIiItnvXMQ57p91PxO3TATgtfteY+XTKwnwDMj2axmGQWRkJJGRkXftj3cXF5g8GebNgxkzkpJ05QoiOcfR0REwKwFF7CnxO5j4ncyqDA8cl9yff/7Jr7/+StWqVW3bqlWrxsSJE+mYyQ5ZNzdpMwwjzWZuCQkJPPPMM7zxxhtUrlw5w+cfNmwYgwcPtr2PjIxUoi4iImIHq0+s5rEFj3Eh+gJerl7M6jSLTlU73bXrOTk5MXDgQNv63ZR8fDrDgKeegqZNzQHmVLsucnc5OTlRqFAhLl68iLOzc7bN5iCSGVarlYsXL1KoUKE7/p2TpaOtVmuaF3ZycsKawc5Yvr6+ODo6pqo1v3DhQpoTxEdGRrJz50727NnDyy+/bIvDMAy8vLz45ZdfaNWqVarjXF1dcXV1zVBMIiIikv2shpUPN37IqFWjsBpWavvXZkGPBVTyqXRXr+vg4EBAQPbX0N/OL7/A99+by4YN8PXX4OmZ42GIFBgWi4XAwEBOnDjBqVOn7B2OFGAODg6UKVPmjsdWyVKS3rJlS1577TVmzpxJYGAgAOfPn+f1119PM1FOi4uLC3Xr1mXVqlUpat9Xr15Nhw4dUpX38vJi27ZtKbZNnTqVtWvX8t1331GuXLmsfBQRERG5i/69/i+9F/dmyZElAPSp04fP239OIedCdo7s7unYET76CF5/HX74AXbuhPnzoUYNe0cmkn+5uLhQuXJlNXkXu3JxccmWlhxZStInTJhAjx49qFatGqVKlcJisXDmzBlq1KjBtGnTMnyewYMH079/f+rWrUujRo2YPn06Z86coX///gCMHj2a8+fP88033+Dg4ECNm367FS9eHFdX11TbRURExP52nN9Bj/k9OP7vcVwdXfms/Wf0q9svx0ZvT0hIYO/evQDUqlXrjvsIZpTFAsOGQePG0LMnHDpkjgb/1VdmM3gRuTscHBw0BZvkC1lK0kuVKsWmTZtYuXIlR44cwTAMqlatSuvWrTN1nm7dunHlyhXef/99QkNDqV69OgsXLqRMmTIAhIaGcvbs2ayEKCIiInZiGAaTt01m2PJhxFnjKFekHAt6LKBeYL0cjSMhIYGff/4ZgOrVq+dYkp6oWTPYtQt69TJHgX/6aTh8GMaOzdEwREQkj7FER0dnavzR+Ph4fHx82Lx5c56swY6IiCAwMJDw8PDbTiIvIiIimfPv9X/p+0tfFh9aDECnqp2Y3nE6Rd2L5ngs8fHxzJs3D4AePXrc9cHj0pOQYCbm770Hq1aZA8qJiEjBEhERgbe3NyEhIbfNQzP928rJyYkyZcqQkJCQ5QBFREQk/9lydguPzX+MU+GncHF0YfyD43mh4Qs51rz9Zk5OTjzxxBN2uXZyjo7w1lvQrx+UKpW0/eRJ0JA6IiJysyz1an/ttdd46623uHLlSnbHIyIiInmM1bDy0caPaD6jOafCT1GxaEU29d3E4EaD7Zag50bJE/QDB6B6dTNxj462X0wiIpL7ZKnd15dffsnx48epVKkSZcqUoVChlCO0btq0KVuCExERkdzt0rVL9F7cm2VHlwHQs0ZPpjwyBS9XdSm7lXXr4MYNmD4dNm2CuXOhdm17RyUiIrlBlpL0Rx55BIvFgmFkqju7iIiI5CPrTq3j8QWPcz7yPG5Obnza9lP61+ufa2rP4+Li+OqrrwB47rnncHZ2tnNESZ57DoKC4Mknk0Z/nzAB/vc/c3R4EREpuDKVpF+7do1Ro0axZMkS4uLiaNWqFR9//DHFihW7W/GJiIhILhNvjee99e/xztp3sBpWqharyrxu86jlX8veoaVgGIata15urFho3Rr27IE+fWDZMhg0yBwF/ptvwMfH3tGJiIi9ZKpP+tixY/nuu+9o27Yt3bt3Z82aNQwdOvQuhSYiIiK5zYl/T9ByZkveWvMWVsNK73t6s/3Z7bkuQQdz4LhnnnmGZ555xm4ju99O8eLw669mLbqzMyxaBNOm2TsqERGxp0xNwVazZk3eeustunfvDsD27dt54IEHuHLlSo7PPZpVmoJNREQka77/+3ueX/Y8ETEReLl68UX7L+hVu5e9w8o3duyAyZPNmvRc+kxBRESyKDNTsGWqJv3s2bM0TTa557333ouTkxMhISFZi1RERERyvfAb4fRa2IsnFz1JREwETUs3ZffA3UrQs1n9+jBzZlKCfuMG9O8PJ07YNSwREclhmUrSExISUg264uTkRHx8fLYGJSIiIrnDhtMbuOere/hh7w84WhwZ02oMa/qsoXzR8vYO7basViv79+9n//79WK1We4eTae+8YzZ9r10bZsyAXNitXkRE7oJMNaYyDIOBAwfi6upq23bjxg2GDBmCh4eHbduPP/6YfRGKiIhIjotLiGPM2jG8t+E9rIaVCkUr8H2X72lcqrG9Q8uw+Ph45s+fD8CIESNwcXGxc0SZM3AgbNhgLn37wpIlMGUKaLxeEZH8LVNJeq9eqZu1PfbYY9kWjIiIiNjfkctHeHrR02w9txWA3vf05tN2n+a5uc8tFgtly5a1rec15crBmjXw0UcwerQ5qNymTebc6u3b2zs6ERG5WzI1cFx+oIHjRERE0mY1rHy27TNeX/E61+Ov4+3qzdcPf03Pmj3tHVqBt2sX9OoFBw+a7z/9FAYPtm9MIiKScXdt4DgRERHJn05ePckD3z7Ai7+/yPX467Sp0Ia9/9urBD2XqFvXHP19yBDw9oaOHe0dkYiI3C1K0kVERAowwzD4Zuc31PqyFmtOrqGQcyG+aP8Fy59cTmnv0vYOT5Jxd4dPPoGjR+G/VvyA2Qw+JsZ+cYmISPbSLJwiIiIF1PnI8zy75FmWHV0GQNPSTZnZaSaVfCrZObLsERcXx7Rp0wDo169fqhlq8qrixZPWly+HLl2gRg1z+rZ777VbWCIikk1Uky4iIlLAGIbB939/T80varLs6DJcHF346MGPWNtnbb5J0MH8nGFhYYSFhWHk0/nLEhLAzw/274fGjWHkSNWqi4jkdRo4TkREpAA5E36G55Y+Z6s9rxdYj287fUsNvxp2jiz7Wa1WTpw4AUD58uVxcMifdROXLpl91RNnwK1e3ZxXvWFD+8YlIiJJNHCciIiIpGA1rHz515fU+KKGrfb83fvfZUu/LfkyQQdwcHCgYsWKVKxYMd8m6GDOm/7DD7BwIfj7w4ED0KQJvP++vSMTEZGsyL+/sURERASAw5cO02pmK55f9jyRsZHcV/o+dg/czRst3sDZMX/00xbo3Nls9v7EE2C1QsWK9o5IRESyQkm6iIhIPhWXEMf7G97nnq/uYf3p9Xg4ezC53WTWP7OeasWr2Tu8u85qtXLkyBGOHDmC1Wq1dzg5wtcXvv8eNm+G7t2Ttm/aBFeu2C8uERHJOCXpIiIi+dD289tp9E0jRqwcQUxCDMEVg9n//H5eaPgCDpaC8es/Pj6eH3/8kR9//JH4+HgsFkuKxdnZmWLFilGrVi369OnDggULiI+Pt1u85cqVw2KxZPn4kydPYrFYaNWqFY0bJ22/dAkefRSqVTP7rdtjDL1WrVql+vk7OjpSrFgxgoOD+eWXX3I+qLso+b+FiEhmaQo2ERGRfOTqjauMWjmKL7d/iYGBj7sPE4Mn8lTtp+4oAcyLLBYLJUqUsK0n6t27N2DWtIeHh3PkyBG+/fZbZs2aRaVKlfj+++9pmI9GXbtwwRwB/sABsyn8t9/CF19A+fI5H0twcDABAQEA3Lhxg4MHD7J8+XKWL1/O2LFjGTVqVM4HJSKSy2h0dxERkXzAMAx+2PsDryx/hbDoMACerP0k4x8cj7+nv52jyx0SE/W0pmM7duwYI0eOZN68eRQqVIiNGzdSp06dHI3v2LFjxMXFUbVq1SwdHxcXx7FjxyhUqBBlypRJsS82Fj78EMaONadoc3eHd96BoUMhJ6aPb9WqFWvXrmX16tWpape//vprnnvuOZydnTl9+rQtic/LTp48Sfny5WnZsiVr1qyxdzgikgtodHcREZEC5NClQ7SZ3YYnFz1JWHQYVXyrsPLplczuPFsJegZVrFiRuXPn0q9fP65du0bfvn3tEkNWE3QAZ2dnqlatmipBB3BxgTfegL//hlat4Pp1eO01qFvXXLengQMHUqZMGeLi4tiyZYt9gxERyQWUpIuIiORR1+Ou88aqN6j9ZW1WnViFm5MbY+8fy57n9tC6fGt7h5cnffzxx3h4eLBr1y42bNiQav/JkycZOHAg5cqVw9XVleLFi9OtWzf+/vvvdM+5efNmevToQYkSJXB1daVkyZIEBwfz3XffpSiXXp/0gwcP8tRTT1GxYkXc3NwoXrw4derUYejQoYSEhKSI7Vb9oGfPnk3fvs3YscMLF5dCODrWplChcVgsN1KV7dOnDxaLhTVr1rBu3Tpat25N4cKF8fLyokOHDhw4cCDdz5sVfn5+AGmOCXDt2jXeffddatasibu7O97e3rRo0YI5c+akeS6LxUK5cuXS3Ddz5kwsFgtvv/12iu2JfeZPnjzJ4sWLady4MR4eHvj4+PD4449z9uzZNM936dIlBg4cSEBAAIUKFaJu3bp8++236X7Oq1evMnnyZIKDgylbtiyurq74+vrStm1b/vzzzzSPSR7bDz/8QOPGjSlcuDBFihThr7/+wmKx0LRp03Sv+c4772CxWBg7dmy6ZUQkd1GSLiIikscYhsGCAwuo/kV1/m/9/xFnjaN95fbsf34/o1qMwtXJ1d4h5gpxcXFMnz6d6dOnExcXl6FjvL29adeuHQCrV69OsW/Dhg3cc889TJkyBU9PTzp27EjlypVZuHAhjRs3TlUeYNKkSTRt2pSffvqJUqVK0aVLF6pWrcrOnTt54403bhvPzp07qV+/Pt9//z3Fixenc+fONGrUiNjYWD755BMOHz6coc81cOBAnn76aXbs2EHz5s3p2LEDRYqE8NdfI2ndujXXr1/nn3/ggw/MpvGJlixZQuvWrbly5QrBwcEEBgaybNkyWrRoQWhoaIaufTuRkZEcOXIEgGrVqqXa16JFC0aPHs2FCxd4+OGHadq0Kdu2bePxxx9n6NCh2RJDoi+++IKuXbtiGAZt27bF09OTOXPm2H5GyV2+fJmmTZsyZcoUnJ2d6dixI97e3jzzzDN89NFHaZ5/y5YtDBkyhIMHD1K5cmU6d+5MlSpVWL58OcHBwUyfPj3d2MaNG8dTTz2Fi4sLDz/8MDVr1qRBgwbUr1+fTZs2sX///lTHWK1WZsyYgaOjI88888yd/XBEJOdER0cbBWkJCQkxACM8PNwQERHJa3aH7DZazWxl8DYGb2OUmlDKWHBggWG1Wu0dWq4TExNjvP3228bbb79txMTEGIAB3Pa4sWPHGoDx+OOP27aFh4cbAQEBhrOzs/HTTz+lKP/nn38aLi4uRsmSJY2YmBjb9rVr1xoWi8Xw8vIyVq9enSq233//PcW2smXLpoqvd+/eBmAsWLAgVZwHDhwwzp8/b3t/4sQJAzBatmyZotz8+fMNwChZsqRx9OjRFJ+pWbNmBmAMG/aq0a6dYYBhBAUZxoMPmtd1cHAwfvjhB9sx8fHxRteuXQ3AePPNN9P5CabWsmVLA0jxc7h+/bqxe/duo127dgZgdOzYMdVxL7zwggEYbdq0MSIjI23bDx48aPj5+RmAsXTp0hTHAEbZsmXTjGPGjBkGYLz11ltpxufh4WGsXLnStj06Otq47777DMCYNm1aimMGDBhgAMajjz5q3Lhxw7Z92bJlhpOTU5r/FsePHzc2btyYKq6dO3caRYoUMby8vFJ8zuSxubm5GWvWrEl17JQpUwzAGDp0aKp9v/32mwEYjzzySJo/DxHJOeHh4QZghISE3DZnVU26iIhIHnAx+iL/+/V/1JtSjzUn1+Dm5MabLd7k0KBDdKnWpcCN3J4RTk5O9OzZk549e+LklPEJbYoVKwbAv//+a9s2ffp0QkNDGTZsGN26dUtRvk2bNjz//POcO3eOX3/91bb9/fffxzAMRo8enaoJuouLC8HBwbeN5cKFCwC0bp26+0K1atUIDAy87Tk+/fRTAMaMGUOlSpVs2728vPjiiy+wWCx8/fVXdOsWi78/HDkCiS2vH374CR5//HHbMY6OjowcORKAdevW3fbaN7v//vttU7C5u7tTp04dVqxYwejRo5k3b16KstHR0UybNg0HBwe++OILPD09bfuqVq1qa4mQ+Pmyw0svvZTiZ12oUCFeeeUVIOXnjYqKYvbs2Tg5OfHpp5/i6prUeqVdu3Z0Tz5JfTLly5fnvvvuS7W9bt26DBo0iIiIiDRbZAD069ePli1bptr+xBNP4OXlxezZs4mJiUmx75tvvgHg2WefTe8ji0gupCRdRETkLoiLg19+ga5dzemusnyehDg+2fIJQZ8F8dWOr7AaVnrU6MGhQYcYc/8YPFw8si/ofMbBwYGqVatStWpVHBwy/ieP8d/o78kffCT2F+7UqVOaxzRr1gyAv/76C4CEhATbqN4DBgzIbOg29evXB+Dpp59m27ZtWK3WTB2fOBibxWLhiSeeSLW/Vq1a1K5dm8jISGrV2sPhw/DSS5D40X/99SGGDoUrV5KOCQoKAkjRHz6jgoOD6d27N7179+app57igQcewMXFhQkTJvD111+nKLtjxw6uX79Ow4YNqVy5cqpzPfXUUwBs3LgxzRH7s+Khhx5KtS2tz7tz506uX79Oo0aN0hyoL/mDjZslJCSwfPly3n77bZ577jn69OlDnz59bMn50aNH0zyuY8eOaW738PCgV69eXL58mUWLFtm2X7hwgV9++YUSJUrQvn37dOMRkdxH86SLiIhko717YcYMmDkTEitiDQOefz5z5zEMg6VHl/Lqn69y6NIhAOoE1OGTtp/QomyL7A1aUrh06RIAPj4+tm0nT54EoFGjRhk69tKlS1y/fh0/Pz8KFy6c5VheffVVNmzYwJIlS1iyZAne3t40atSIhx9+mD59+tz23JcvXyY2NpaAgADc3NzSLFOuXDn27NnD+fPnadAAJkyAEydg8WKwWkvxySdQujT8V6Fsq9G+udY2I15//fVUrQouXrxI27ZtefHFFylWrJjtYcL58+dt8aWlSJEieHt7Ex4ebpva6E6VKlUq1ba0Pm9ibGkl6LfafvbsWR5++GH27NmTbgyRkZGZOifAc889x5dffsnUqVN57LHHAHOQvLi4OPr27Yujo2O6x4pI7qMkXURE5A5dugQ//gjffGNOceXkBImDVDs6mnNSZ8aWs1sYvmI4606ZzWuLFSrGe63fo2/dvjg66I/tjLJarZw+fRq4dYJzs927dwNQvXp127aEhAQAunfvTqFChdI99uYk/k67IXh5ebFq1So2btzIkiVLWLNmDStXrmT58uWMGzeO9evXU7FixdueJyNxJC+TmO+OH29h7VoYNCip3H8t8LNN8eLFGTNmDA8//DAff/xxqhr/zMZ+K7driZDR86TV2iIj+vfvz549e+jSpQvDhw+nSpUqFC5cGAcHB6ZMmcLAgQPTbRWQ3kMWgNq1a9sGLzx27BgVK1Zk2rRpWCwW+vXrl6kYRcT+7J6kT5kyhUmTJhEaGkq1atX48MMP051G4ueff2bq1Kns3buXmJgYqlWrxsiRI3nwwQdzOGoRESno4uLg999h+nT49Vf4L4cDkhJ0MJsNZzRJP3zpMKNWjWLBwQUAuDq6MqTREEY2H0kRtyLZF3wBER8fz6xZswAYMWJEho4JDw/n999/B8z+04lKlSrF4cOHeeONN6hdu/Ztz1OsWDHc3d0JCwsjMjLyjmrTLRYLzZo1szWpv3jxIi+++CI//vgjI0eOZO7cueke6+vri4uLC6GhoVy/fh33NL6Mp06dAkizf3v9+kk16GB+txN/LFmoSE9X+fLlAVKMVl+iRAkATpw4keYx4eHhhIeH4+HhkeLn6+zsTFRUVJrHnDlzJlviTYwt8Wd3s8SHQ8lFR0fz559/4u/vz7x581LVbh8/fvyOYnruuefYsmUL06ZNIzg4mCNHjvDQQw+l2xJBRHIvu/ZJnz9/Pq+99hqvvfYamzZt4r777qNz587p3kA3bNhA69atWbhwIRs2bKBFixZ0797d9sRbRETkbtu710xaAgKgY0czQY+PN5u0p1UBZrHA+vXw7LPw4ovw+uvwzjvw4YcwebJZ+/75tKsEj/ya6i+9woJll+BsIx4t8gZ/djjBi9U/xHqtCNevp31+SZ/FYqF48eIUL148wzWer7zyCtHR0TRo0IAmTZrYtrdp0waAxYsXZ+g8jo6OtmbdU6dOzVTct1O8eHHbPN979+69ZVlnZ2caN26MYRj8+OOPqfbv27ePPXv2ULhwYe65557bXnv3brMpPEBoKDzyCNyi5XaGJSaoHh5JYyzUr18fd3d3tm3blmY/7cR55ps1a5bi3zcwMJDLly9zJXlH+v8sX778zoP9LzY3Nze2bt2a5t+tac3hHh4ejtVqJTAwMFWCHh8fn6I/eVb06NGDokWLMnPmTL788ktAA8aJ5FV2rUmfPHkyvXv3pk+fPgB89NFHrFy5kqlTpzJmzJhU5W+ec/Kdd95h6dKl/Pbbb9SpUycHIhYRkYLo8uWk5ux79phN2BNrzpPXmqclLg6OHYPjx5MG4wIz4U6wGhhWC1AEGPjfYvr5v+VmLi7g6gpubuZSqFDS4uFhLu7uqZdChdLefquybm6QifHWch1nZ2eez+BgAMePH2fEiBHMmzcPDw8Ppk2blmL/wIEDmTBhAu+99x6lS5emT58+KRLD6OhoFixYQOvWrW39mocPH87vv//Ou+++S4MGDWjevLmtfFxcHKtWrbrtCO9fffUVwcHBtprmRL/99huQsWb8gwcPZt26dbz11lu0atWKChUqAGbf5xdeeAHDMBg4cCAuLi63Pde995qjv5cubb7/9Vdzefxx8+FTGuO73dbFixd56623AFIMcObh4UHfvn35/PPPGTRoEIsWLbIl8UeOHGHs2LG2z5dcy5YtmT17Nu+++y4TJ04EzObp77//Pps2bcp8gGnw9PSkV69eTJs2zdaqIXGE9+XLl6caqR7Az88Pb29v9u3bx8aNG20tRxMSEnjttddsc8Vnlbu7O08//TSffPIJc+fOpXjx4jz66KN3dE4RsQ+7JemxsbHs2rXLNq1FotatW7N169YMncNqtRIZGUnRokXTLRMTE5NioI/0BuMQERG52cGDMGoULFmSsjl78vWMSL985vsrx8aay61+nTk4mMvNDwWsVnPJDGfnlA8FEpP4mx8KZOYhwK0eIOTE+FaJlQNWq5WIiAiOHDnCoUOHMAyDypUr88MPP1CrVq0UxxQtWpRFixbRsWNH+vbtyzvvvEPNmjVxdXXl9OnTHDx4kOjoaHbt2mVL0lu2bMmHH37Iq6++SosWLWjYsCEVK1bkwoUL7NmzBw8PD9uAdOn56quv+N///kf16tWpVq0aTk5OHD58mN27d+Pu7m5Lbm+lW7duDBgwgClTplCzZk1at25NoUKFWLNmDRcvXqRx48a88847Gf75JY6tVrIkNGsGc+eaD7HmzTMfYtWokf6x77//PjNnzgTMn39ISAibN28mOjqaihUr8t5776UoP27cOLZs2cKff/5JhQoVaNmyJdHR0axatYobN24wZMgQOnTokOKY4cOHM3/+fCZNmsSaNWuoWLEie/fu5cyZMzz//PN8cSfTLdz0WdauXcuiRYuoXLkyTZs2JSwsjLVr1zJw4EBbbXYiJycnXnvtNUaNGkXLli1p3bo1Pj4+bN26lbCwMAYNGsTnn39+RzENHDiQTz75BDC/587Oznd0PhGxD7sl6ZcvXyYhIQE/P78U2/39/VmxYkWGzvHJJ59w7do1unTpkm6Z8ePHp7rhi4iIZMT69XCHLVDtIivJeHri4swlnS6+QPY+FHByMh8KJD4YSO+hwO1aCNStC+m13k7sp+7k5ISXlxclSpTg6aefpmPHjnTs2DHdOdWbNm3K3r17mTBhAkuXLmXVqlU4OjpSokQJHn74Ybp06ZJisDmAYcOG0aBBAyZOnMimTZvYtWsXfn5+1K9fn6effvq2P493332XxYsXs3XrVlauXElsbCylSpViwIABvPrqqynmPb+Vr7/+mmbNmvHVV1+xdu1a4uPjqVixIkOHDuWll15Ks6/67Tg5wZw5ZheON94wHxwl//jXr6cej+GPP/5I8d7T05OgoCA6duzIyy+/jJeXV4r9hQsXZu3atXz88cfMnTuXX375BRcXF+69916ef/75NKc6q1GjBqtWrWLEiBFs27aN48eP07RpU+bNm8euXbsy/TnTU6xYMTZu3MioUaP45ZdfWLx4MUFBQUydOpXWrVunStIBRo4cSalSpZg0aRIbN27E3d2dZs2aMWbMGHbu3HnHMVWrVo0SJUpw/vx5+vfvf8fnExH7sERHR9ulh1tISAiVKlVi1apVKUZC/fDDD/nxxx9vexOdN28egwYNYu7cubRu3TrdcmnVpAcFBREeHp7qF4GIiMjN9u2Djz6CH374r4l6JmvRJfslPhBI3hQ/cUwAq9V8rVYN9uyJs/UNfuyxx1SreJddu2Y+NAGzi0jVqtCjBwwfDpkYXF/uwKZNm2jatCktW7ZkzZo19g5HRJJJnCoyJCTktnmo3Xqa+fr64ujoSFhYWIrtFy5cSFW7frP58+fz/PPPM3v27Fsm6ACurq54eXnZljsZXVVERAqemjVh1ixzsKyhQ80kJC/3084PrFbzYUliLX9cnDk2QEJC0uB6FovZD/n48eMcP3483WmtJPskn5luwQJzasIvvoBKlcyBE+9w8HLJgMTWoy+88IKdIxGRO2G3PzNcXFyoW7cuq1atSrF99erVqeYYTW7evHkMHDiQGTNm0LZt27sdpoiICGD2wx0/Hs6fh3HjoHhxc/ttBw23pKx6t1gMHB3NpsLOzubi5GT2xb7DKbUlGQ8Pszl7586d6dy5c7pN2OXuePZZWL0aWrc2H6J88w0EBUHv3pBsljXJBps2baJfv340atSIpUuXUr9+/Vt2BRWR3M9uzd3BrBHv378/n3zyCY0aNWL69OnMnDmT7du3U6ZMGUaPHs358+f55ptvADNBf/bZZ/noo4/o2LGj7Tzu7u54e3tn6JoREREEBgaqubuIiNyRmBizCfy4cXD0aMoR32/Wvvd+HmtTldgYR65f55bLtWsQHW0u166Zy40bSUtsbOb6eSc2C7dYkh4C3Nw0PD9q2RLU2jd32LQJ3n0X/pt+Hjc3CAmBIkXsGla+MXPmTJ555hkKFy5Mq1at+OyzzzI06r+I5KzMNHe3a5IOMGXKFCZOnEhoaCjVq1fngw8+oFmzZgAMGDCA06dP8/t/d/W2bduyfv36VOfo1asXU6ZMydD1lKSLiEh2slrhs++P8+7/xXHpcBWwxIGRsu/z0qWQbGapO2IYZs3krZL82z0IuN1DgevXzQcCMTHmkpl++Gk9FEiMOzsHtLud9u3Nn7vkHn/9BWPHgq8vTJ+etH3jRmjSRN1IRCR/y1NJek5Tki4iItkhwZrA0qNL+WTrJ6w68V/XrbMN8d89kbAdTXByhPh4M0tdtQruv9+Owd6h+Pg7exhwc9n0HgokPhi43dzzN7t5dPn4eOjaFebONaf4AggMDMRBWWCuEB9vdvEAc2DGWrXM+dVfeQWefjr1iPAiIvlBZpJ0ddASERHJhIiYCKbvms7kbZM5/q85EpajxZHuNbrz+sDXuSfgHo4eNfuvz5hh1nrn9TFLnZzMz5BTnyMhIesPABKXbt0gPj7e1mVuxIgRuLi45MwHkFtKPjzA4cNms/ejR+G558yp3AYNgoEDITDQbiGKiNiVatJFREQy4Ojlo0zeNpkZu2cQFWtOGl7UrSjP1nuWQQ0HUcY7dR/QCxfMWvQePdSU1x7i4uL4/PPPARg0aJCmYMuloqLM5u8TJ8LJk+Y2Jyfo0gUmT4bbTPojIpInqLn7LShJFxGRjIq3xvPb0d/4asdX/Hb0NwzMX5nVi1dnSMMhPFn7STxcPOwcpUj+EB8PCxfCp5+a/dT9/eH0aUhsAGEYmgFBRPIuNXcXERG5A2fCz/DNzm+Ytmsa5yLP2bZ3qNyBFxu9SJsKbbAoWxDJVk5OZquTHj1gzx44dSopQU9IgPr1oUULs1l89er2jVVE5G5STbqIiAhJteZTdk5h2dFlWA1zGPJihYrR554+DKg/gMq+le0cpUjB9Mcf0LZt0vvGjaFvX+jZE/TnnIjkBWrufgtK0kVEJLnDlw4z++/ZzNozi7MRZ23b7y93PwPqD6Bz1c64OrnaMULJqvj4eObPnw9At27dcHJSA8K8ymqFFSvgiy/g11+TpgUsVAi6d4fXX4eqVe0bo4jIrai5u4iIyC1cuX6FufvmMmvPLLae22rb7uvuS586Zq15kG+QHSOU7GC1Wjl8+LBtXfIuBwd46CFzCQ2F2bNh2jRzdPhZs+D555PKJiSAo6P9YhURuVNK0kVEpECITYjlt6O/8e3f37Lk8BLirHGAOX1acKVgnq79NJ2qdlKteT7i6OjIww8/bFuX/CEgAF59FYYNg82bYelSaNAgaf/AgeaUbk88Yday+/jYL1YRkaxQc3cREcm34q3xrDm5hnn757Hw4EIuX79s21cnoA5P136ax2s9ToBngB2jFJHsEhdnTtl29ar53tnZ7Mveqxc88ojZPF5ExB7U3F1ERAqsBGsC606tY+7+uSw4uIBL1y7Z9gV4BvBkrSd56p6nqO1f245Risjd4OwMf/8Nc+bADz/A7t2wZIm5eHrC0KHw7rv2jlJE5NaUpIuISJ4XlxDH+tPrWXBgAfMPzudC9AXbPl93X7pW60qPGj1oWa4lTg761VdQGIbBxYsXAShevLimzSsgSpc2m8O/+iocOGAm6z/8ACdOmH3bE127Bj//DB06aIR4Ecld1NxdRETypIiYCH7/53d+OfwLS48u5eqNq7Z9Rd2K0qVaF3rW6Emrcq1wdnS2X6BiN7GxsYwbNw6AESNG4JI46bYUOIYBW7ZAyZJQpoy5beFC6NrVnIv9wQehSxezSXzx4vaNVUTyJzV3FxGRfOlsxFl+OfwLvxz+hVUnVtkGfwNzPvNHgh6hR40ePFD+ASXmAkAhdUIWwGKBJk1SbktIgCpVzBHily41F4sFGjWChx+G/v3B398+8YpIwaaadBERybVi4mPYcHoDfxz7gz+O/cHfYX+n2F/ZpzKPVnmUR6s+SpNSTXB00AjeIpJxhgEHD8KCBWbN+u7dSfuOH4fy5c3106fB1xc8POwSpojkA6pJFxGRPMkwDP658g9/HPuD3//5ndUnV3Mt7pptvwULTUo3oWNQRx6t+ihVi1W1Y7QiktdZLFC9urm8+SacOwfLlpnJemKCDjB4MPz+OzRtCm3amM3j69XTfOwicneoJl1EROwqJDKEtafWsubkGpYfW86JqydS7A/wDCC4YjDBFYN5sOKDFCtUzE6RikhBZLXCPffAvn0ptxcpAq1bQ/v20K+fXUITkTxENekiIpJrhUaFsvbkWlafXM2ak2s4fPlwiv3ODs40K9OM4IrBtK3Ultr+tTUqt2RJfHw8v/zyCwAdO3bEyUl/9kjmOTiY07r98w/8+SesWAGrVplzsS9cCFeupEzS582DOnWgcmWzpl5EJLP020pERO4awzA49u8xNp/ZzMYzG1l7ai2HLh1KUcaChToBdWhVrhX3l7uf+8vfj6eLp50ilvzEarWyd+9eAB5++GE7RyN5mcViJt2VK8Pzz0N8POzYYSbs5collbt0CXr2NNf9/aF586Sldm01jxeRjFGSLiIi2SY6Nprt57ez+exmNp3ZxJazW7h47WKKMsmT8lblWtG8THOKuhe1U8SSnzk6OhIcHGxbF8kuTk7mKPCNGqXcfvGimZBv3QphYTB/vrmAORf7u+/CkCE5H6+I5C1K0kVEJEvirfEcvnSYHSE72HZuG5vPbmZP6B4SjIQU5VwcXagfWJ8mpZrQomwLmpdtjo+7j52iloLE0dGRxo0b2zsMKUCqVYN16+DGDfjrL1i/3lw2boSICChcOKnstm3w+ONmot+woflaty64udkvfhHJHZSki4jIbcUlxHHg4gF2huxkR8gOdoTsYE/oHq7HX09VtmThkjQp3YQmpZpwX+n7qBtQF1cnVztELSJiH25uSc3cwWwe//ffULp0UpktW8xp3o4fhx9/NLc5OZmD1NWrBy+8YDaRF5GCR0m6iIikcOnaJfZd2MfesL3su7CPXaG7+Dvsb2ISYlKV9XTxpG5AXbOm/L/EvLR36TTOKpLzDMMgPDwcAG9vbw1AKHbj5GQm3sn17g1Vq5o16lu3msvFi2Zf9x074Kmnksr+8gt8/71Z016njrkEBOTkJxCRnKQkXUSkgIqKjeLAxQO2ZHzfRTMxD4sOS7O8t6s39QLrUS+wHvUD61MvsB6VfSvjYHHI4chFMiYuLo5PPvkEgBEjRuDi4mLniESSeHvDQw+ZC4BhwKlTZjP53bvNGvVEq1ebo8bPm5e0rVixpDneR42CUqVyNHwRuYuUpIuI5GNWw8rZiLMcvnSYI5ePcPhy0uvJqyfTPa5C0QrU9KtJLb9a1PavTf3A+pQvWl4JueQ5zs7O9g5BJEMsFnOk+HLloHv3lPueeAICA83kffduOHzYHEl+3TpzGT06qey4cbB0qZm816hh1tZXqgRly5o1+iKS++m/qohIHmc1rIREhnD83+OcuHoiRTJ+9PLRNPuNJwrwDKCWXy1q+tW0JeXVilfTFGiSL7i4uDBy5Eh7hyFyxxo0MJdE166Zifr+/XD0aMqm71u2mAPVbdyY8hzOzlC+PGzeDD7/jd159Kg5LVzZspoeTiQ3sURHRxv2DiInRUREEBgYSHh4OF5eXvYOR0QkQ/69/i8nrp7gxL8nbMn4iavm+qmrp9LsL57I2cGZij4VCfINoopvFar4ViHIN4hqxatRrFCxHPwUIiJytx08aNa2HzhgJvFHjsA//0BMDLi7Q3S0WWsP0LUrLFxoJvCJtfhlyya9PvaYat9FsktERATe3t6EhITcNg/VfzsRETuLjInkbMRZzkSc4WzEWduS+P5M+BnCY8JveQ5HiyOlvUtTvkh5gnyDkhLyYlUoV6QcTg663YuIFATVqplLclYrnDtnLsnHTzQMcHU1E/ijR80lkZsb9OqV9H7wYDPxL1cOypSBkiWhRAnztWRJ8PVNeW4RyTr91SYichcYhkF4TDhhUWGERoUSFm2+hkaFEhYVxrnIc7YkPCImIkPn9Pfwp3zR8pQv8t9StDwVilagfJHylPYurURc5Cbx8fEsW7YMgPbt2+OkKkEpoBwczOnfSt80+cbChWYCf/asORXcyZPm4HUnT0JCQsqke/Nmc9T5tCTW0CcaPx5CQpKS+MBA8Pc3lyJFlMyL3I5+W4mIZND1uOtcvn6ZS9cucfnaZS5fv8zF6Iu2BPzmRPxWTdBvVsStCKW8SlHKqxSlvUrb1hOXst5l8XDxuIufTiT/sVqt7Nq1C4C2bdvaORqR3MnBwawZL1Pm1uU++8ysaT95Es6cMWvlz583X29OvOfMST+h9/U1B71LNGEChIaaCbyfX9JrsWJm3/lChe70E4rkPUrSRaRAMQyDqNgowmPCuXrjKuE3wgmPCefK9Sspku/L1y9z+dp/Cfl/67cagC09Xq5eBHgG4O/hb3v19/SnZOGSlPY2k/GShUtS2LXwXfi0IgWbo6Mj999/v21dRLKucWNzSUt8fMr3zz0Hhw4lNbEPCzOX8HAoWjRl2e+/h5070z5v0aJw5UrS+1dfNWv8fXzMxdc36dXXF1q0yPrnE8lNlKSLSJ5gNaxEx0YTFRuV5hIeE25LuK/euJoqCU++bjWsWY7DycEJX3dfihUqhm8h8zXAIwB/T/+UybinP/4e/rg7u2fjT0FEMsPR0ZEW+qtd5K67uSdJ//5pl7txAyJu6uH17LPm4HZhYXDhQtLr5ctJo9AnWrUq/YS+SBH499+k98HBsG2bOR+9tzd4eSWt+/rCp58mlV23zozLy8tcPD3BwyPp1UGzj0oOs3uSPmXKFCZNmkRoaCjVqlXjww8/pGnTpumWX79+Pa+//joHDx4kMDCQl156if7p3QlEJEdYDSs34m9wPe461+Ov217T2pZ837W4a+km3VGxUUTHJSXl1+KuZWvMjhZHirgVwdvNG29Xb3zcfcyk291MvpMn4r7uvraEvLBLYSzqTCciIpJpbm7mktxzz6Vd1jDg+k0N2MaMMfvMX7liJvHJXz1vmjn0yhW4etVcbla0aMokfcwYWLky7TicnCA2Nqk5/4svwtatKZN4T8+k9bffTprObtMm86GDu7v5uW9+LVVKDwAkbXZN0ufPn89rr73GpEmTaNy4MdOmTaNz587s2LGD0jePbAGcPHmSLl260KdPH6ZNm8aWLVsYOnQoxYoVo1OnTjn/AURygGEYJBgJxFvj011iE2KJTYglJj7Gth6bEEtMQsr3GS5z07aY+BhuxN8wk+40Eu7YhNgc+3k4WBzwdPG0LR7OHni6eOLl6mUm3a7eeLt533a9kHMhJdsi+ZxhGFy7Zj7gK1RI/+dF8hKLJXV/9A4dMn78r7+aNevh4eYSEZG0fvOtoEqVpH2RkeYgeFFR5oMCD4+U5Q8cMJP0tDg4mAl/ovHjYdGi9GOMjk76jP36wU8/pUzkk68vWmS2AgCYORPWrwcXF3N0fheXpMXVFf73P7NFAMD27eZYAsn3Jy9fs2bSg5PwcLh2zXwwkdaiW2jOses86S1btqROnTp88skntm316tXj4YcfZkzyb/h/3njjDZYtW8bOZO1chgwZwt69e1m9enWGrpkf5kk3DAMDI8Wr1bCm2paVV6thveNzZHc8VsNKgjUhad1IyHXbE4wEEqxmIh1njbtlQp2RJS4h6RwJRoK9v3KZ4uTghLuTO+7O7ile3ZzcUm1zd3KnsGvhNJPu9BY3Jzf9oS0iGRIbG8u4ceMAGDFiBC4uLnaOSETyCsMwm+dfu2Y2j0+0fbs5YF5UVFIyn7geFwcff5xUdsQIsyn99evmuW5+vXYtqSa9e3eYPz/9eCIioPB/w9f07QszZqRf9vx5c0R9gCFDYPLk9MsePQqVKiXF+/776ZfdvRvuucdcHz/eLOvsnHZC/913SWXnzYOvvkpd1tHRXEaNMh8WAKxdCz/+aG53cEgqk7g8/XTSFIN795oPYxwdYcAAs8tDbpYn5kmPjY1l165dvPLKKym2t27dmq3pPJ7atm0brVu3TrGtTZs2zJo1i7i4OJydnVMdExMTQ0xM0gjLkZGR2RD93Td7z2z6/tI3VdIqksjB4oCTgxOOFkdcnVxxcXSxLa6OKd+7OLpkrMxN25If4+romiLJdnNyS5WMuzm5aRowERERyfMslqTa7OTuvTfj5/jvGWGGfPmlWf769ZTJfOJ68lYF3bpB5cpmM/zEJSYmaT150//KlaF165T7k5dP3v3AMMyENyGd+qHkqVZkpNnVID2xyRpZnjoFt6pPHTAgaX3fPvj66/TLNm2alKTv2AEjR5rr3bvn/iQ9M+z21/Tly5dJSEjAz88vxXZ/f39WrFiR5jFhYWH4+/un2Obn50d8fDyXLl0iMPGRUTLjx4/nvffey77Ac4jVsBJvjb99wWxkwYKDxQGLxYIFyx29Olgc7vgcifE4OjiarxbzNfm2O96ejed0cnBKtTg7Oqe5PbOLs0PK8yReW0RE0ufi4sJbb71l7zBERG6rWDFzyYj27c0lIwYPNpeMeP99czEMM1GPjzdbB8THm0vykfkHD4aePVOXSXxfpUpS2UcegdKlU+6PiwOr1bxO5cpJZRs2hHfeSdp381KhQlLZSpXMVgUJCUmtDPILu1d53dxs1TCMTDVlNQwjzfMkGjZsGIOTfTMjIyMJCgrKQqQ5q1v1brSp0CZTyeydJMQiIiIiIiIWS1KT9JsH+kuUmYcKVauaS0Y0aGAuGdGsmbnkR3ZL0n19fXF0dCQsLCzF9gsXLqSqXU/k7++fqvzFixdxcnLCN3lnkWRcXV1xdXXNnqBzkIeLBx4uHvYOQ0RERERERHKQ3drLuri4ULduXVatWpVi++rVq2nUqFGaxzRs2DDVAHErV66kXr16afZHFxEREREREclL7NqpdfDgwcycOZNZs2Zx6NAhXnvtNc6cOWOb93z06NEp5kDv378/p0+fZvjw4Rw6dIhZs2Yxa9YsXnzxRXt9BBEREREREZFsY9c+6d26dePKlSu8//77hIaGUr16dRYuXEiZMmUACA0N5ezZs7by5cqVY+HChQwfPpwpU6YQGBjI+PHjNUe6iIiIiIiI5At2nSfdHvLDPOkiIiIiIiKSd2RmnnTN4SQiIiIiIiKSSyhJFxEREREREckllKSLiIiIiIiI5BJ2HTjOHgzD7IIfERFh50hERERERESkIEjMPxPz0VspcEl6VFQUAKVLl7ZzJCIiIiIiIlKQREVF4e3tfcsyBW50d6vVSkhICJ6enlgsFnuHc0uRkZEEBQVx5MgRChcubO9wJA/Qd0YyQ98XySx9ZySz9J2RzNJ3RjIrr3xnDMMgKiqKwMBAHBxu3eu8wNWkOzg4ULJkSXuHkSmFCxfWdHGSKfrOSGbo+yKZpe+MZJa+M5JZ+s5IZuWF78ztatATaeA4ERERERERkVxCSbqIiIiIiIhILqEkPRdzdXVl5MiRuLq62jsUySP0nZHM0PdFMkvfGcksfWcks/SdkczKj9+ZAjdwnIiIiIiIiEhupZp0ERERERERkVxCSbqIiIiIiIhILqEkXURERERERCSXUJIuIiIiIiIikksoSbejKVOmUL16dXx8fGjatCkbN268Zfn169fTtGlTfHx8qFGjBt98800ORSq5RWa+M+vWrcPDwyPVcvjw4RyMWOxpw4YNdOvWjYoVK+Lh4cGSJUtue4zuMwVbZr8zus8UbB999BHNmzfH39+fsmXL0rNnT44cOXLb43SfKbiy8p3RfaZgmzp1Kg0bNiQgIICAgADuv/9+/vjjj1sekx/uMUrS7WT+/Pm89tprvPbaa2zatIn77ruPzp07c+bMmTTLnzx5ki5dunDfffexadMmXn31VYYNG8bixYtzNnCxm8x+ZxLt3r2bY8eO2ZZKlSrlUMRib9HR0dSqVYsJEyZkqLzuM5LZ70wi3WcKpg0bNjBgwABWr17NkiVLiI+Pp2PHjkRHR6d7jO4zBVtWvjOJdJ8pmEqWLMmYMWNYv34969evp2XLlvTs2ZMDBw6kWT6/3GM0BZudtGzZkjp16vDJJ5/YttWrV4+HH36YMWPGpCr/xhtvsGzZMnbu3GnbNmTIEPbu3cvq1atzJGaxr8x+Z9atW0e7du04d+4cRYoUycFIJTfy8PBgzpw5PPLII+mW0X1GksvId0b3GUnu4sWLlCtXjj/++INmzZqlWUb3GUkuI98Z3WfkZqVKleL//u//6N27d6p9+eUeo5p0O4iNjWXXrl088MADKba3bt2arVu3pnnMtm3baN26dYptbdq0YefOncTFxd21WCV3yMp3JtF9991HhQoVaN++PWvXrr2bYUoep/uMZJXuMwIQEREBQNGiRdMto/uMJJeR70wi3WckISGBn376iejoaBo2bJhmmfxyj1GSbgeXL18mISEBPz+/FNv9/f0JCwtL85iwsDD8/f1TbPPz8yM+Pp5Lly7dtVgld8jKdyYgIIDPPvuM77//nh9//JGgoCA6dOjAhg0bciJkyYN0n5HM0n1GEhmGweuvv859991HjRo10i2n+4wkyuh3RvcZ2bdvH35+fhQtWpQXX3yRH3/8kWrVqqVZNr/cY5zsHUBBZrFYUrw3DCPVtlsxDCPN80j+lZnvTFBQEEFBQbb3jRo14uzZs3zyySfpNikTuZnuM3Irus9Iopdffpl9+/axYsWKTB+r+0zBlNHvjO4zEhQUxObNmwkPD2fx4sUMHDiQ33//Pd1E/WZ58R6jmnQ78PX1xdHRMVUN6IULF1LVlCZKq8b04sWLODk54evre9dildwhK9+ZtDRs2JBjx45ld3iST+g+I9lB95mC55VXXmHp0qX89ttvlCxZ8pZldZ8RyNx3Ji26zxQsLi4uVKxYkXr16jFmzBhq1qzJF198kWbZ/HKPUZJuBy4uLtStW5dVq1al2L569WoaNWqU5jENGzZMNdjBypUrqVevHs7OznctVskdsvKdScuePXtSNQESSaT7jGQH3WcKDsMwePnll/n5559ZtmwZ5cqVu+0xus8UbFn5zqRF95mCzTAMYmJi0tyXX+4xau5uJ4MHD6Z///7UrVuXRo0aMX36dM6cOUP//v0BGD16NOfPn7fN69e/f3++/vprhg8fzjPPPMPWrVuZNWsWM2fOtOOnkJyU2e/MZ599RtmyZalWrRqxsbHMmTOHxYsX88MPP9jzY0gOioqKSlHTcPLkSfbs2YOPjw+lS5fWfUZSyex3RveZgu2ll15i3rx5zJ07F09PT0JDQwHw9vbG3d0d0N8zklJWvjO6zxRsb731Fg899BClSpUiMjKS+fPns379etuUavn1HqMk3U66devGlStXeP/99wkNDaV69eosXLiQMmXKABAaGsrZs2dt5cuVK8fChQsZPnw4U6ZMITAwkPHjx9OpUyc7fQLJaZn9zsTGxjJy5EjOnz+Pu7s71apVY8GCBbRt29ZeH0Fy2M6dO2nXrp3t/euvvw5Ar169mDJliu4zkkpmvzO6zxRsU6dOBUj17/3VV1/x1FNPAfp7RlLKyndG95mC7cKFC/Tv35/Q0FC8vLyoWbMmixcvts14lF/vMZonXURERERERCSXUJ90ERERERERkVxCSbqIiIiIiIhILqEkXURERERERCSXUJIuIiIiIiIikksoSRcRERERERHJJZSki4iIiIiIiOQSStJFREREREREcgkl6SIiIiIiIiK5hJJ0ERGRfObUqVN4eHiwZ8+ebDnf//3f/9G4ceNblhkwYAA9e/a8ZZl169bh4eHB1atXb3vNhx56iLlz52YmzExr3rw5P//88129hoiISGYpSRcREblLBgwYgIeHBx4eHnh7e1OjRg1GjBhBdHR0ho7PTFJ7N7344ossXbo0U8e0bduWV199NUvX++233wgLC6N79+5ZOj6jXn/9dUaPHo3Var2r1xEREckMJekiIiJ30YMPPsixY8fYv38/o0ePZurUqYwcOdLeYWWKp6cnvr6+OXa9L774gieffBIHh7v7Z0rbtm0JDw/nzz//vKvXERERyQwl6SIiIneRq6srAQEBlCpVip49e9KzZ0+WLFkCgGEYTJgwgRo1auDr60ujRo1YtGgRYDZZb9euHQAlS5bEw8ODAQMGALB8+XLatGlDiRIlKF26NF27duX48eMZjunLL7+kQYMGtvdLlizBw8ODr7/+2ratY8eOjB49Gkjd3D0hIYHhw4fbrj9q1CgMw7DtHzBgAOvXr+eLL76wtSQ4deqUbf+uXbto1qwZxYoVo3Xr1hw5csS279KlS6xevZoOHTqkiPnq1au88MILlCtXDh8fH+69915+++03AGbPnk2JEiX47bffqFOnDsWKFaNXr15ER0fz3XffUa1aNUqWLMkrr7xCQkKC7ZyOjo4EBwfz008/ZfhnJyIicrcpSRcREclB7u7uxMfHw/+3d28hUX1tHMe/4/lUHtLJEx6yyFBRNBHUkSyoK8moIKMiKYgiEexCCzMkosCKTPMqRaishA4XoVBR4AweSku6SCNMZCiSClPQDGXe9yLcNG/9S/tnCe/vAwOy91rPWrNu5NnPXmuAyspKLl++zLlz5+ju7ubgwYPs2bMHq9VKZGQkTU1NAPT29jIwMEBVVRUAExMTFBUV0dbWxp07d3BxcWHbtm2zfm3bYrHQ19fH+/fvAbBarQQHB2Oz2QCYnp6mq6uL7Ozs7/avrq7m0qVL1NXVce/ePUZGRowHDwBVVVVkZGRQWFjIwMAAAwMDREZGGvcrKys5efIkVqsVNzc39u/fb9zr6OjAx8eH+Ph445rD4WDTpk10dnZSX19PT08Px48fd6q0T0xMUFdXR2NjI7dv38ZqtVJQUMDdu3e5efMmFy9epKGhwXgIMmP16tW0t7fPat1ERET+BLe/PQEREZH/F93d3TQ3N7NmzRrGx8epqamhpaWFjIwMAGJjY+no6KC+vh6LxUJgYCAAISEhBAQEGHHy8/Od4tbV1RETE0NfXx8JCQk/ncdM5d5ms5Gfn4/VaqWoqIja2loAenp6mJycJDMz87v9L1y4wKFDh4x5nD9/nvv37xv3/f398fDwwNvbm9DQ0G/6Hzt2DIvFAkBJSQmbN29mcnISLy8vhoaGMJvNTgn4gwcP6O7u5smTJ6xYscJYq69NTU1RXV3NsmXLjDW6evUqg4OD+Pn5sWrVKnJycmhra2PLli1Gv/DwcOx2Ow6HY95frxcREZkN/TcSERGZR62trZjNZoKCgsjNzSUrK4vTp0/T39/P5OQkeXl5mM1m49PU1MTg4OAPY7569Yrdu3eTkJBAaGiokZjb7fZZzclkMpGVlYXVauXjx4/09fWxd+9eHA4H/f39tLW1kZKSgp+f3zd9R0dHefv2rfFgAcDNzY3U1NRZr0liYqLx90wS/+7dOwA+ffqEl5eXU/tnz54RERFhJOjf4+PjYyToAGazmejoaKfvYDabjXFmeHl54XA4+Pz586znLyIiMp9USRcREZlHOTk5VFdX4+7uTlhYGO7u7gDGHu0bN24QHh7u1MfT0/OHMbdu3UpERAS1tbWEhYXhcDhIT09nampq1vOyWCw0NDTQ3t5OUlISAQEBZGVlYbPZsFqtRqV7PsysAXx5YAAYr+oHBwczMjLi1N7b23tOMWfiurm5fXPtf7cEjIyM4OPjM6sxRERE/gRV0kVEROaRr68vcXFxREVFOSWS8fHxeHp6YrfbiYuLc/rM7N/28PAAcDrs7MOHD/T391NaWkpubi7x8fG/9BNtM/vSb926ZSTk2dnZPHz48If70f39/QkNDeXRo0fGtenpaZ4+ferUzt3d/Zd+2iw5OZnh4WGnRD0xMZHXr1/z8uXLOcf7mefPn5OSkvLb44qIiPwqVdJFRET+gkWLFlFcXExZWRkOh4PMzEzGxsbo6urC19eXHTt2EBUVhclkorW1lQ0bNuDt7U1gYCBLliyhoaGB0NBQ7Ha7cQr7XMzsS79+/TrNzc3Al8T98OHDAP+4Hx3gwIEDnD17luXLl7Ny5UpqamoYHR11ahMdHc3jx48ZGhrC19eXoKCgWc0rOTmZ4OBgOjs7jdPtLRYL2dnZbN++nVOnThEXF8eLFy8wmUysX79+zt/9a+3t7axbt+5fxRAREfmdVEkXERH5SyoqKigrK+PMmTOkpqayceNGWlpaiImJAb4calZeXk5FRQWxsbGUlJTg4uJCY2Mjvb29pKenU1payokTJ+Y8tslkMqrlMwl5UlIS/v7+JCcns3jx4n/sW1xcTEFBAfv27WPt2rX4+fmRl5f3TRtXV1fS0tKIjo6e9X55V1dXdu3axbVr15yuX7lyhbS0NAoLC0lLS6O8vPyXKvVfe/PmDZ2dnezcufNfxREREfmdTOPj4//5eTMRERGRP2N4eJj09HRsNhtRUVHzNs6RI0cYGxszTrUXERFZCFRJFxERkQVl6dKl1NXVzbr6/qtCQkI4evTovI4hIiIyV6qki4iIiIiIiCwQqqSLiIiIiIiILBBK0kVEREREREQWCCXpIiIiIiIiIguEknQRERERERGRBUJJuoiIiIiIiMgCoSRdREREREREZIFQki4iIiIiIiKyQChJFxEREREREVkglKSLiIiIiIiILBD/BW5QplpAiTBEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1200x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_range = np.linspace(0,3,1000).reshape(-1,1)\n",
    "y_proba = logis_reg.predict_proba(X_range)\n",
    "\n",
    "mid = None\n",
    "for i in range(len(X_range)):\n",
    "    if y_proba[i,1] - y_proba[i,0] <= 0.000001:\n",
    "        mid = X_range[i,0]\n",
    "\n",
    "%matplotlib inline\n",
    "fig, ax = plt.subplots(1,1, figsize=(12,3),\n",
    "                       facecolor='whitesmoke',\n",
    "                       edgecolor='gray')\n",
    "ax.plot(X_range, y_proba[:,1],'g-',label=\"Iris-Virginica\")\n",
    "ax.plot(X_range, y_proba[:,0],'b--',label=\"Not Iris-Virginica\")\n",
    "ax.vlines(mid, 0, 1,lw=1.5, ls=':', color='gray')\n",
    "ax.annotate(text=\"Decision Boundary\", xytext=(mid,0.2), xy=(mid-0.4,0.2),\n",
    "            arrowprops = {'headwidth':10,'facecolor':'b','edgecolor':'b'},fontsize = 15)\n",
    "ax.annotate(text=\"\", xytext=(mid,0.9), xy=(mid+0.4,0.9),\n",
    "            arrowprops = {'headwidth':10,'facecolor':'g','edgecolor':'g'},fontsize = 15)\n",
    "ax.set_xlabel(\"Petal width(cm)\")\n",
    "ax.set_ylabel(\"Probability\")\n",
    "ax.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4129efa4",
   "metadata": {},
   "source": [
    "# Softmax Regression\n",
    "1. also called Multinomial Logistic Regression\n",
    "2. ova combinations\n",
    "3. combination function - normalized exponential\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "    s_{k}(x) & = & \\theta^{T} \\cdot x \\\\\n",
    "    \\hat p_{k} & = & {\\sigma[s(x)]}_k = \\frac{exp[s_{k}(x)]}{\\sum_{j=1}^{K}{exp[s_{j}(x)]}}\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "4. here $\\theta$ is a $(k,m)$ matrix, k means k-classes and m means m features, $x$ is still a $(m,n)$ data matrix with each column symbolizes one data entry, final output $s_{k}(x)$ is a $(k,n)$ matrix\n",
    "5. for training, all target should be processed into one-hot form, then \n",
    "6. cost function (similar to logistic regression, instead of binomial distribution, it's a multinomial distribution)\n",
    "$$\n",
    "    J(\\theta) = -\\frac{1}{m}\\sum_{k=1}^{K}{y_k \\cdot log(\\hat p_{k})}\n",
    "$$\n",
    "7. derivitive form of cost function\n",
    "$$\n",
    "    \\frac{\\partial J(\\theta)}{\\partial \\theta_{k}} = \\frac{1}{m}[\\hat p_{k} - y_{k}]\\cdot x\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "0f05a557",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, multi_class='multinomial')"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# select 2 different features: petal length, petal width\n",
    "X_sft = raw_iris[\"data\"][:,(2,3)]\n",
    "# 3 classes, and will be transferred into one-hot form\n",
    "y_sft = raw_iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class='multinomial',solver=\"lbfgs\", C=10)\n",
    "softmax_reg.fit(X_sft,y_sft)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "59c509a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x7f8c608f6850>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx_sft = np.linspace(0,7,100)\n",
    "yy_sft = np.linspace(0,3.5,100)\n",
    "\n",
    "xx, yy = np.meshgrid(xx_sft, yy_sft)\n",
    "zz = np.zeros_like(xx)\n",
    "for x_idx in range(len(xx_sft)):\n",
    "    for y_idx in range(len(yy_sft)):\n",
    "        zz[x_idx, y_idx] = softmax_reg.predict([[ yy_sft[y_idx],xx_sft[x_idx]]])\n",
    "\n",
    "fig,ax = plt.subplots(1,1,facecolor='whitesmoke',edgecolor='grey',\n",
    "              figsize=(8,3))\n",
    "#ax.scatter()\n",
    "ax.contourf(xx,yy,zz,cmap=plt.cm.autumn_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a9f67cc",
   "metadata": {},
   "source": [
    "## Hardmax Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "829a26ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "var = tf.constant([2,3,6,10.4,5,1],dtype=tf.float32)\n",
    "pr = tf.nn.softmax(var)\n",
    "print(pr)\n",
    "print(tf.argmax(pr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "38e9bc80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9991570000000001"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "math.pow(0.551,2) + math.pow(0.834,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c6a7bd0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "python3.6",
   "language": "python",
   "name": "python3.6"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "315.594px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
